Two astronauts on opposite ends of a spaceship are comparing lunches. One has an

Question

Two astronauts on opposite ends of a spaceship are comparing lunches. One has an apple, the other has an orange. They decide to trade. Astronaut 1 tosses the 0.130 kg apple toward astronaut 2 with a speed of vi,1 = 1.09 m/s. The 0.170 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.22 m/s. Unfortunately, the fruits collide, sending the orange off with a speed of 0.977 m/s in the negative y direction.

http://session.masteringphysics.com/problemAsset/1123753/2/Walker4e.ch09.Pr041.jpg

A) What are the final speed and direction of the apple in this case?

Explanation / Answer

Using conservation of momentum

(x-direction) m1*v1i + mi*v2i = m1*v1f + m2*v2f

v1f = 0.130kg*1.09m/s - 0.170kg*1.22 = 0.130kg*v1f + 0.170*0

 

(y-direction) m1*v1i + mi*v2i = m1*v1f + m2*v2f

v1f = 0.130kg*0 + 0.170kg*0 = 0.130kg*v1f - 0.170kg*.977m/s

 

total v = (v1fx^2 + v1fy^2)^.5

direction -->   = tan^-1(v1fy/v1fx)

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