# What are the final speed and direction (theta) of the apple in this case?

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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 0.120kg apple toward astronaut 2 with a speed of vi,1 = 1.05m/s . The 0.170kg 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 0.889m/s in the negative y direction.

In this collision problem, the total momentum would be conserved $P_i=P_f$.
Assume astronaut 1 is on the left and 2 on the right. So the velocity of the apple is in +x direction and the velocity of the orange is towards -x. The momentum before collision:$$\sum P_{xi}=M_a(1.05)+M_o(-1.19)$$ $$\sum P_{yi}=0$$
After the collision,  $$\sum P_{yf}=0=M_o(-0.889)+M_a(V_{ay})$$ and $$\sum P_{xf}=M_a(V_{ax})+M_o(0)=M_a(1.05)+M_o(-1.19)$$
From these you can solve for $V_{ax}$ and $V_{ay}$ to get the magnitude and angle.