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 = 1.06 m/s . The 0.160 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.23 m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 1.01 m/s in the negative y direction.What are the final speed and direction of the apple in this case?

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Explanation / Answer

ince there was no y momentum (Ly) originally then it must stay at 0 so

L(orange) = 0.160*(-1.01) = -0.1616 kg-m/s

now Ly(apple) = 0.1616 = 0.130*vy

==> vy = 0.1616/0.130 = 1.24m/s (+y)

The initial momentum x momentum = 0.160*1.23 - 0.130*1.06 = 0.059 (Assuming the + x direction is the initial direction of the orange)

The final x momentum = 0.059 = 0.130*v1x => v1x = 0.059/.0130 = 4.53m/s (in the direction of the orange originally) (i.e the apple is going backwards)

So v apple = sqrt(4.53^2 + 1.24^2) = 4.69m/s

the angle arctan(vy/vx) = arctan(1.24/4.53) = 15.3o

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