Unit 1 Kinematics 1 - Walking the Dog You and your dog go for a walk to the park. On the way, your dog takes many side trips 1) yes to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? 2) no 1 - Walking the Dog You and your dog go for a walk to the park. On the way, your dog takes many side trips 1) yes to chase squirrels or examine fire hydrants. When you arrive at the park, do you and 2) no your dog have the same displacement? Yes, you have the same displacement. Since you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement. Follow-up: Have you and your dog traveled the same distance? 2 - Displacement Does the displacement of an object depend on the specific location of the 1) yes 2) no 3) it depends on the origin of the coordinate system? coordinate system 2 - Displacement Does the displacement of an object 1) yes depend on the specific location of the 2) no origin of the coordinate system? 3) it depends on the coordinate system Since the displacement is the difference between two 1 0 2 0 3 0 4 0 5 0 3 0 4 0 5 0 6 0 7 0 coordinates, the origin does not matter. 3 - Position and Speed 1) yes If the position of a car is zero, 2) no does its speed have to be 3) it depends on the zero? position 3 - Position and Speed 1) yes If the position of a car is zero, 2) no does its speed have to be 3) it depends on the zero? position No, the speed does not depend on position, it depends on the change of position. Since we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = –3 and be moving by the time it gets to x = 0. 4 - Odometer Does the odometer in a car 1) distance measure distance or 2) displacement displacement? 3) both 4 - Odometer Does the odometer in a car 1) distance measure distance or 2) displacement displacement? 3) both If you go on a long trip and then return home, your odometer does not measure zero, but it records the total miles that you traveled. That means the odometer records distance. Follow-up: How would you measure displacement in your car? 5 - Speedometer Does the speedometer in a car measure velocity or speed? 1) velocity 2) speed 3) both 4) neither 5 - Speedometer Does the speedometer in a car measure velocity or speed? 1) velocity 2) speed 3) both 4) neither The speedometer clearly measures speed, not velocity. Velocity is a vector (depends on direction), but the speedometer does not care what direction you are traveling. It only measures the magnitude of the velocity, which is the speed. Follow-up: How would you measure velocity in your car? 6 - Acceleration I 1) yes If the velocity of a car is non-zero (v ≠0), 2) no can the acceleration of the car be zero? 3) depends on the velocity 6 - Acceleration I 1) yes If the velocity of a car is non-zero (v≠ 0), 2) no can the acceleration of the car be zero? 3) depends on the velocity Sure it can! An object moving with constant velocity has a non-zero velocity, but it has zero acceleration since the velocity is not changing. 7 - Acceleration II When throwing a ball straight up, which of the following is true about 1) both v = 0 and a = 0 2) v ≠ 0, but a = 0 3) v = 0, but a ≠ 0 its velocity v and its acceleration a at 4) both v ≠0 and a ≠ 0 the highest point in its path? 5) not really sure 7 - Acceleration II When throwing a ball straight up, 1) both v = 0 and a = 0 which of the following is true about 2) v ≠ 0, but a = 0 its velocity v and its acceleration a at 3) v = 0, but a ≠ 0 4) both v ≠0 and a ≠ 0 the highest point in its path? 5) not really sure At the top, clearly v = 0 because the ball has momentarily stopped. But the velocity of the ball is changing, so its acceleration is definitely not zero! Otherwise it would remain at rest!! Follow-up: …and the value of a is…? y 8 - Free Fall I You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value of acceleration? 1) its acceleration is constant everywhere 2) at the top of its trajectory 3) halfway to the top of its trajectory 4) just after it leaves your hand 5) just before it returns to your hand on the way down 8 - Free Fall I You throw a ball straight up 1) its acceleration is constant into the air. After it leaves everywhere your hand, at what point in 2) at the top of its trajectory its flight does it have the 3) halfway to the top of its trajectory maximum value of 4) just after it leaves your hand acceleration? 5) just before it returns to your hand on the way down The ball is in free fall once it is released. Therefore, it is entirely under the influence of gravity, and the only acceleration it experiences is g, which is constant at all points. 9 - Free Fall II Alice and Bill are at the top of a 1) Alice’s ball building. Alice throws her ball 2) it depends on how hard downward. Bill simply drops his the ball was thrown ball. Which ball has the greater 3) neither -- they both have acceleration just after release? the same acceleration 4) Bill’s ball Alice v Bill 0 v v A B 9 - Free Fall II Alice and Bill are at the top of a 1) Alice’s ball building. Alice throws her ball 2) it depends on how hard downward. Bill simply drops his the ball was thrown ball. Which ball has the greater 3) neither -- they both have acceleration just after release? the same acceleration 4) Bill’s ball therefore they both feel the acceleration due to Alice v gravity (g). This acceleration is independent of the 0 Both balls are in free fall once they are released, initial velocity of the ball. v v A B Follow-up: Which one has the greater velocity when they hit the ground? Bill 10 - Up in the Air I You throw a ball upward with an initial speed of 10 m/s. Assuming 1) more than 10 m/s 2) 10 m/s 3) less than 10 m/s that there is no air resistance, what is its speed when it returns to you? 4) zero 5) need more information 10 - Up in the Air I You throw a ball upward with an initial speed of 10 m/s. Assuming 1) more than 10 m/s 2) 10 m/s that there is no air resistance, 3) less than 10 m/s what is its speed when it returns 4) zero to you? 5) need more information The ball is slowing down on the way up due to gravity. Eventually it stops. Then it accelerates downward due to gravity (again). Since a = g on the way up and on the way down, the ball reaches the same speed when it gets back to you as it had when it left. 11 - Up in the Air II Alice and Bill are at the top of a cliff of height 1) vA < vB H. Both throw a ball with initial speed v0, Alice straight down and Bill straight up. The 2) vA = vB speeds of the balls when they hit the ground 3) vA > vB are vA and vB. If there is no air resistance, 4) impossible to tell which is true? Alice v 0 v Bill H 0 v v A B 11 - Up in the Air II Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed v0, Alice 1) vA < vB straight down and Bill straight up. The speeds 2) vA = vB of the balls when they hit the ground are vA 3) vA > vB and vB. If there is no air resistance, which is 4) impossible to tell true? Bill’s ball goes up and comes back down downward with v0, the same as Alice’s Alice v 0 v ball. Thus, it will hit the ground with the 0 same speed as Alice’s ball. v v A B to Bill’s level. At that point, it is moving Bill H Follow-up: What happens if there is air resistance? 12 - Throwing Rocks I You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their separation? 1) the separation increases as they fall 2) the separation stays constant at 4 m 3) the separation decreases as they fall 4) it is impossible to answer without more information 12 - Throwing Rocks I You drop a rock off a bridge. 1) the separation increases as they fall When the rock has fallen 4 m, you drop a second rock. 2) the separation stays constant at 4 m As the two rocks continue to 3) the separation decreases as they fall fall, what happens to their 4) it is impossible to answer without more separation? information At any given time, the first rock always has a greater velocity than the second rock, therefore it will always be increasing its lead as it falls. Thus, the separation will increase. 13 - Throwing Rocks II You drop a rock off a 1) both increase at the same rate bridge. When the rock has 2) the velocity of the first rock increases faster fallen 4 m, you drop a than the velocity of the second second rock. As the two 3) the velocity of the second rock increases rocks continue to fall, what faster than the velocity of the first happens to their velocities? 4) both velocities stay constant 13 - Throwing Rocks II You drop a rock off a 1) both increase at the same rate bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their velocities? 2) the velocity of the first rock increases faster than the velocity of the second 3) the velocity of the second rock increases faster than the velocity of the first 4) both velocities stay constant Both rocks are in free fall, thus under the influence of gravity only. That means they both experience the constant acceleration of gravity. Since acceleration is defined as the change of velocity, both of their velocities increase at the same rate. Follow-up: What happens when air resistance is present? 14 - Graphing Velocity I 1) it speeds up all the time The graph of position versus 2) it slows down all the time time for a car is given below. 3) it moves at constant velocity What can you say about the 4) sometimes it speeds up and velocity of the car over time? sometimes it slows down 5) not really sure x t 14 - Graphing Velocity I 1) it speeds up all the time The graph of position versus 2) it slows down all the time time for a car is given below. 3) it moves at constant velocity What can you say about the 4) sometimes it speeds up and velocity of the car over time? sometimes it slows down 5) not really sure x The car moves at a constant velocity because the x vs. t plot shows a straight line. The slope of a straight line is constant. Remember that the slope of x versus t is the velocity! t 15 - Graphing Velocity II The graph of position vs. time 1) it speeds up all the time 2) it slows down all the time for a car is given below. What 3) it moves at constant velocity can you say about the velocity 4) sometimes it speeds up and of the car over time? sometimes it slows down 5) not really sure x t 15 - Graphing Velocity II 1) it speeds up all the time The graph of position vs. time 2) it slows down all the time for a car is given below. What 3) it moves at constant velocity can you say about the velocity 4) sometimes it speeds up and of the car over time? sometimes it slows down 5) not really sure The car slows down all the time because the x slope of the x vs. t graph is diminishing as time goes on. Remember that the slope of x vs. t is the velocity! At large t, the value of the position x does not change, indicating that the car must be at rest. t 16 - v versus t graphs I 1) decreases Consider the line labeled A in the 2) increases v versus t plot. How does the 3) stays constant speed change with time for line 4) increases, then decreases A? 5) decreases, then increases v A t B 16 - v versus t graphs I 1) decreases Consider the line labeled A in the 2) increases v versus t plot. How does the 3) stays constant speed change with time for line 4) increases, then decreases A? 5) decreases, then increases v A In case A, the initial velocity is positive t B and the magnitude of the velocity continues to increase with time. 17 - v versus t graphs II 1) decreases Consider the line labeled B in the 2) increases v versus t plot. How does the 3) stays constant speed change with time for line 4) increases, then decreases B? 5) decreases, then increases v A t B 17 - v versus t graphs II 1) decreases Consider the line labeled B in the 2) increases v versus t plot. How does the 3) stays constant speed change with time for line 4) increases, then decreases B? 5) decreases, then increases v In case B, the initial velocity is positive A but the magnitude of the velocity t B decreases toward zero. After this, the magnitude increases again, but becomes negative, indicating that the object has changed direction. 18 - Rubber Balls I v v 1 3 t v 2 You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this motion? (Assume your y-axis is pointing up.) t t 4 v t 18 - Rubber Balls I v v 1 3 t v 2 You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this t t v 4 The ball is dropped from rest, so its initial velocity is zero. Since the y-axis is pointing upwards and the ball is falling downwards, its velocity is negative and becomes more and motion? (Assume your y-axis is more negative as it accelerates downward. pointing up.) t 19 - Rubber Balls II v v 1 3 t v 2 You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the above plots represents the v vs. t graph for this motion? (Assume your y-axis is pointing up.) t v 4 t t 19 - Rubber Balls II v v 1 3 t v 2 You toss a ball straight up in the air t v 4 t t The ball has an initial velocity that is positive and catch it again. Right after it leaves your hand and before you but diminishing as it slows. It stops at the top (v catch it, which of the above plots = 0), and then its velocity becomes negative and represents the v vs. t graph for this becomes more and more negative as it motion? (Assume your y-axis is pointing up.) accelerates downward. 20 - Rubber Balls III v v 1 3 t v 2 You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this motion? t t 4 v t 20 - Rubber Balls III v v 1 3 t v 2 You drop a very bouncy rubber ball. It falls, and then it hits the floor and t t v 4 t Initially, the ball is falling down, so its velocity must be negative (if UP is positive). Its velocity is also increasing in magnitude as bounces right back up to you. Which it falls. Once it bounces, it changes direction of the following represents the v vs. and then has a positive velocity, which is t graph for this motion? also decreasing as the ball moves upward. 21 - Rubber Balls IV v v 1 3 t v 2 You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this motion? t t 4 v t 21 - Rubber Balls IV v v 1 3 t t v 2 You drop a very bouncy rubber ball. It falls, and then it hits the floor and v 4 t Initially, the ball is falling down, so its velocity must be negative (if UP is positive). Its velocity is also increasing in magnitude bounces right back up to you. t as it falls. Once it bounces, it changes Which of the following represents direction and then has a positive velocity, the v vs. t graph for this motion? which is also decreasing as the ball moves upward. 22 - Vectors I 1) same magnitude, but can be in any direction If two vectors are given such 2) same magnitude, but must be in the same that A + B = 0, what can you direction 3) different magnitudes, but must be in the same say about the magnitude and direction direction of vectors A and B? 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions 22 - Vectors I If two vectors are given such 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same that A + B = 0, what can you direction say about the magnitude and 3) different magnitudes, but must be in the direction of vectors A and same direction B? 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other, in order for the sum to come out to zero. You can prove this with the tip-to-tail method. 23 - Vector Components I If each component of a 1) it doubles vector is doubled, what 2) it increases, but by less than double happens to the angle of 3) it does not change 4) it is reduced by half that vector? 5) it decreases, but not as much as half 23 - Vector Components I If each component of a 1) it doubles vector is doubled, what 2) it increases, but by less than double happens to the angle of 3) it does not change that vector? 4) it is reduced by half 5) it decreases, but not as much as half The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan θ = 2y/2x, which is the same as tan θ = y/x (the original angle). Follow-up: If you double one component and not the other, how would the angle change? 24 - Vector Components II A certain vector has x and y components that 1) 30° are equal in magnitude. Which of the following 2) 180° is a possible angle for this vector, in a 3) 90° standard x-y coordinate system? 4) 60° 5) 45° 24 - Vector Components II A certain vector has x and y components 1) 30° that are equal in magnitude. Which of the 2) 180° following is a possible angle for this vector, 3) 90° in a standard x-y coordinate system? 4) 60° 5) 45° The angle of the vector is given by tan θ = y/x. Thus, tan θ = 1 in this case if x and y are equal, which means that the angle must be 45°. 25 - Vector Addition You are adding vectors of length 20 and 40 units. What is the only 1) 0 2) 18 possible resultant magnitude that 3) 37 you can obtain out of the following 4) 64 choices? 5) 100 25 - Vector Addition You are adding vectors of length 20 and 40 units. What is the only 1) 0 2) 18 possible resultant magnitude that 3) 37 you can obtain out of the following 4) 64 choices? 5) 100 The minimum resultant occurs when the vectors are opposite, giving 20 units. The maximum resultant occurs when the vectors are aligned, giving 60 units. Anything in between is also possible, for angles between 0° and 180°. 26 - Firing Balls I A small cart is rolling at constant 1) it depends on how fast the cart is velocity on a flat track. It fires a moving ball straight up into the air as it 2) it falls behind the cart moves. After it is fired, what 3) it falls in front of the cart happens to the ball? 4) it falls right back into the cart 5) it remains at rest 26 - Firing Balls I A small cart is rolling at constant 1) it depends on how fast the cart is velocity on a flat track. It fires a moving ball straight up into the air as it 2) it falls behind the cart moves. After it is fired, what 3) it falls in front of the cart happens to the ball? 4) it falls right back into the cart 5) it remains at rest In the frame of reference of the cart, the ball only has a vertical component of velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart. when viewed from train when viewed from ground 27 - Firing Balls II Now the cart is being pulled along 1) it depends upon how much the track a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the is tilted 2) it falls behind the cart 3) it falls in front of the cart cannon as it moves. After it is 4) it falls right back into the cart fired, what happens to the ball? 5) it remains at rest 27 - Firing Balls II Now the cart is being pulled along a 1) it depends upon how much the track horizontal track by an external force is tilted (a weight hanging over the table edge) and accelerating. It fires a ball 2) it falls behind the cart straight out of the cannon as it 3) it falls in front of the cart moves. After it is fired, what 4) it falls right back into the cart happens to the ball? 5) it remains at rest Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the first question), so it will lag behind the accelerating cart once it is shot out of the cannon. 28 - Dropping a Package You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all 28 - Dropping a Package You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: 1) quickly lag behind the plane while falling 2) remain vertically under the plane while falling 3) move ahead of the plane while falling 4) not fall at all Both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the xdirection, so they stay aligned. Follow-up: What would happen if air resistance is present? 29 - Dropping the Ball I From the same height (and at (1) the “dropped” ball the same time), one ball is (2) the “fired” ball dropped and another ball is (3) they both hit at the same time fired horizontally. Which one (4) it depends on how hard the ball will hit the ground first? was fired (5) it depends on the initial height 29 - Dropping the Ball I From the same height (and at (1) the “dropped” ball the same time), one ball is (2) the “fired” ball dropped and another ball is (3) they both hit at the same time fired horizontally. Which one (4) it depends on how hard the ball will hit the ground first? was fired (5) it depends on the initial height Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant – remember that the x and y motions are completely independent !! Follow-up: Is that also true if there is air resistance? 30 - Dropping the Ball II 1) the “dropped” ball In the previous problem, 2) the “fired” ball which ball has the greater 3) neither – they both have the velocity at ground level? same velocity on impact 4) it depends on how hard the ball was thrown 30 - Dropping the Ball II 1) the “dropped” ball In the previous problem, 2) the “fired” ball which ball has the greater 3) neither – they both have the velocity at ground level? same velocity on impact 4) it depends on how hard the ball was thrown Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground. Follow-up: What would you have to do to have them both reach the same final velocity at ground level? 31 - Dropping the Ball III A projectile is launched from 1) just after it is launched the ground at an angle of 30o. 2) at the highest point in its flight At what point in its trajectory 3) just before it hits the ground does this projectile have the 4) halfway between the ground and the least speed? highest point 5) speed is always constant 31 - Dropping the Ball III A projectile is launched from the 1) just after it is launched ground at an angle of 30o. At 2) at the highest point in its flight what point in its trajectory does 3) just before it hits the ground this projectile have the least speed? 4) halfway between the ground and the highest point 5) speed is always constant The speed is smallest at the highest point of its flight path because the y-component of the velocity is zero. 32 - Punts I Which of the 3 punts has the h longest hang time? 1 2 4) all have the same hang time 3 32 - Punts I Which of the 3 punts has the h longest hang 1 time? 2 4) all have the same hang time The time in the air is determined by the vertical motion ! Since all of the punts reach the same height, they all stay in the air for the same time. Follow-up: Which one had the greater initial velocity? 3 33 - Punts II A battleship simultaneously fires two shells at two enemy submarines. The shells are launched with the same initial velocity. If the shells follow the trajectories shown, which submarine gets hit first ? 1 2 3) both at the same time 33 - Punts II A battleship simultaneously fires two shells at two enemy submarines. The shells are launched with the same initial velocity. If the shells follow the trajectories shown, which submarine gets hit first ? The flight time is fixed by the motion in the y-direction. The higher an object goes, the longer it stays in flight. The shell hitting ship #2 goes less high, therefore it stays in flight 1 for less time than the other shell. Thus, ship #2 is hit first. 2 3) both at the same time Follow-up: Which one traveled the greater distance? 34 - Cannon on the Moon For a cannon on Earth, the cannonball would follow path 2. Instead, if the same cannon were on the Moon, where g = 1.6 m/s2, which path would the cannonball take in the same situation? 1 2 3 4 34 - Cannon on the Moon For a cannon on Earth, the cannonball would follow path 2. Instead, if the same cannon were on the Moon, where g = 1.6 m/s2, which path would the cannonball take in the same situation? The ball will spend more time in the air because gMoon < gEarth. With more time, it 1 2 can travel farther in the horizontal direction. Follow-up: Which path would it take in outer space? 3 4 35 - Spring-Loaded Gun The spring-loaded gun can launch 1) 15° projectiles at different angles with the same 2) 30° launch speed. At what angle should the 3) 45° projectile be launched in order to travel the 4) 60° greatest distance before landing? 5) 75° 35 - Spring-Loaded Gun The spring-loaded gun can launch 1) 15° projectiles at different angles with the same 2) 30° launch speed. At what angle should the 3) 45° projectile be launched in order to travel the 4) 60° greatest distance before landing? 5) 75° A steeper angle lets the projectile stay in the air longer, but it does not travel so far because it has a small x-component of velocity. On the other hand, a shallow angle gives a large x-velocity, but the projectile is not in the air for very long. The compromise comes at 45°, although this result is best seen in a calculation of the “range formula” as shown in the textbook. 36 - Shoot the Monkey I You are trying to hit a friend with a 1) yes, it hits water balloon. He is sitting in the 2) maybe – it depends on window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the the speed of the shot 3) no, it misses 4) the shot is impossible 5) not really sure water balloon hit him? Assume that the shot does have enough speed to reach the dorm 36 - Shoot the Monkey I You are trying to hit a friend with a 1) yes, it hits water balloon. He is sitting in the 2) maybe – it depends on window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the Yourwater friend falls under the balloon hit him? influence of gravity, just like the water balloon. Thus, they are both undergoing free fall in the ydirection. Since the slingshot was accurately aimed at the right height, the water balloon will fall exactly as your friend does, and it the speed of the shot 3) no, it misses 4) the shot is impossible 5) not really sure Assume that the shot does have enough speed to reach the dorm 37 - Shoot the Monkey II You’re on the street, trying to hit a 1) yes, it hits friend with a water balloon. He sits in 2) maybe – it depends on his dorm room window above your the speed of the shot position. You aim straight at him and 3) the shot is impossible shoot. Just when you shoot, he falls 4) no, it misses out of the window! Does the water 5) not really sure balloon hit him?? Assume that the shot does have enough speed to reach 37 - Shoot the Monkey II You’re on the street, trying to hit a 1) yes, it hits friend with a water balloon. He sits in 2) maybe – it depends on his dorm room window above your the speed of the shot position. You aim straight at him and 3) the shot is impossible shoot. Just when you shoot, he falls 4) no, it misses out of the window! Does the water 5) not really sure balloon hit him?? This is really the same situation as before!! The only change is that the initial velocity of the water balloon now has a y-component as well. But both your friend and the water balloon still fall with the same acceleration -- g !! Assume that the shot does have enough speed to reach 38 - Shoot the Monkey III You’re on the street, trying to hit a friend 1) yes, they hit with a water balloon. He sits in his dorm 2) maybe – it depends on the room window above your position and is speeds of the shots aiming at you with HIS water balloon! 3) the shots are impossible You aim straight at him and shoot and he 4) no, they miss does the same in the same instant. Do 5) not really sure the water balloons hit each other? 38 - Shoot the Monkey III You’re on the street, trying to hit a friend 1) yes, they hit with a water balloon. He sits in his dorm 2) maybe – it depends on the room window above your position and is speeds of the shots 3) the shots are impossible aiming at you with HIS water balloon! You aim straight at him and shoot and he 4) no, they miss 5) not really sure does the same in the same instant. Do the water balloons hit each other? This is still the same situation!! Both water balloons are aimed straight at each other and both still fall with the same acceleration -- g !! Follow-up: When would they NOT hit each other?

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