1. A 90.0-kg astronaut is working on the engines of his ship, which is drfting t

Question

1. A 90.0-kg astronaut is working on the engines of his ship, which is drfting through space with a constant velocity. The astronaut, wishing to get a better view of the Universe, pushes against the ship and much later finds himself 45.0.0m behind the ship and at rest with respect to it. Without a thruster, the only way to retum to the ship is to throw his 1.500-kg wrench directly away from the ship. If he throws the wrench with a speed of 15.0 m/s relative to the ship, how long does it take the astronaut to reach the ship? 2. A 110.0-kg fullback running east with a speed of 6.00 m/s is tackled by a 105.0-kg opponent running north with a speed of 4.00 m/s. If the collision is perfectly inelastic, (a) calculate the speed and direction of the players just after the tackle and (b) determine the energy lost as a result of the collision. Account for the missing energy

Explanation / Answer

1) Using newton's third law, momentum of wrench and astronaut must be equal

mwrench * vwrench = mastronaut * vastronaut

1.5*15 = 90* vastronaut

vastronaut = 0.25 m/s

time taken to reach the ship = 45 / 0.25 = 180 seconds or 3 minutes.

2) As the collision is inelastic , we have

m1v1 + m2v2 = (m1 + m2)vfeast

Note for east direction, v2 = 0 as he is running in north

vfeast = m1v1 / m1+m2

vfeast = 660 / 215 = 3.07 m/s

Now for vfnorth

  vfnorth  = 420 / 215 = 1.953 m/s

Therefore, vf = sqrt(vf2east + vf2north )

(a) vf = 3.638 m/s

theta = arctan ( 1.953 / 3.07) = 32.46 degree

(b) mehcanical energy lost is change in kinetic energy

k.efinal - k.einitial

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