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 1.18 m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 0.964 m/s in the negative y direction.

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

Vf,2 = ??m/s

Part B

counterclockwise from the positive x axis

Explanation / Answer

here,

mass of apple , ma = 0.13 kg

mass of ornage , mo = 0.17 kg

intial speed of apple , ua= 1.09 i m/s

initial speed of orange , uo = - 1.18 i m/s

final speed of orange , vo = - 0.964 j m/s

let the final speed of apple be va

using conservation of momentum

ma*ua + mo*uo =ma*va + mo*vo

0.13 * 1.09 i - 0.17 * 1.18 = - 0.13*0.964 j + 0.17 vo

vo = (- 0.346 i + 0.765 j )m/s

vo = sqrt(0.346^2 + 0.765^2)

vo = 0.84 m/s

theta = arctan( 0.346/0.765)

theta = 24.34 degree

the final speed is 0.84 m/s and 155.66 degree counterclockwise from +x axis

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