Homework 7 Problems: Linear Momentum 1. An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she’s on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12.0-kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to propel herself back toward it. a. [5 points] Determine the maximum distance she can be from the craft and still return within 2.00 min. b. [5 points] Explain in terms of Newton’s laws of motion why this strategy works. 2. A pitcher throws a 0.14-kg baseball toward the batter so that it crosses home plate horizontally and has a speed of 42 m/s just before it makes contact with the bat. The batter then hits the ball straight back at the pitcher with a speed of 48 m/s. Assume the ball travels along the same line leaving the bat as it followed before contacting the bat. a. [5 points] What is the magnitude of the impulse delivered by the bat to the baseball? b. [5 points] If the ball is in contact with the bat for 0.0050 s, what is the magnitude of the average force exerted by the bat on the ball? 3. [15 points] Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s. After the collision, the orange disk moves in a direction that makes an angle of 37.0⁰ with the horizontal axis while the green disk makes an angle of 53.0⁰ with this axis. Determine the speed of each disk after the collision. 4. A block with mass m1 = 0.500 kg is released from rest on a frictionless track at a distance h1 = 2.50 m above the top of a table. It then collides elastically with an object having mass m2 = 1.00 kg that is initially at rest on the table. a. [3 points] Describe the motion of the blocks from the point at which block is released until both blocks land on the ground. Describe the energy and momentum transformations that occur throughout the motion of both blocks. b. [3 points] Determine the velocities of the two objects just after the collision. c. [3 points] How high up the track does the 0.500 kg object travel back after the collision? d. [3 points] How far away from the bottom of the table does the 1.00-kg object land, given that the height of the table is h2 = 2.00 m? e. [3 points] How far away from the bottom of the table does the 0.500-kg object eventually land? Bonus: [6 points] For an elastic collision between two objects, we can write the momentum and kinetic energy conservation equations as Show mathematically that these conditions imply for full credit. ( ). Show all of your steps

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