Question

Physics Help Please:

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 0.130kg apple toward astronaut 2 with a speed of vi,1 = 1.07m/s . The 0.160kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.19m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 0.998m/s in the negative y direction.
What are the final speed and direction of the apple in this case?

I already found the speed (1.29m/s) but I cannot find the direction.
Picture is in the reply box.
Thank You

Answer 1

Assume orange is going from left to right and apple is going from right to left
If mv is the momentum of apple at angle θ to the x axis,
In the x direction
0.130*v cos θ = (0.170*1.23) -(0.130*1.08)
0.130*v cos θ = 0.0687-------------------------2

In the y direction
0.130*v sin θ = (0.170*0.974) = 0.16558--------------1

From 1 and 2
tan θ = 2.41

θ = 74.96º
Substituting the value of θ in
0.130*v cos θ = 0.0687

v = 1.38 m/s
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