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 0.130kg apple toward astronaut 2 with a speed of vi= 1.07m/s. The 0.160kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.25m/s. Unfortunately, the fruits collide, sending the orange off with a speed of 1.02m/s in the negative y direction.

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

What is the angle in degrees counterclockwise from the positive x-axis?

Explanation / Answer

Using conservation of momentum:
Before:
x direction: 0.130*1.07 - 0.160 * 1.25 = - 0.0609 [Kg * m / s]
y direction = 0

After:
Vay is velocity of the apple in the y direction
Vax is the velocity of the apple in the x direction

momentum again:
x direction: 0.130 * Vax + 0 = -0.0609 (momentum did not change) hence: Vax = -0.468 [m/s]
y direction: 0.130 * Vay -0.160 * 1.02 = 0 hence Vay = 1.255 [m/s]

so the apple has a speed of sqrt( (-0.468)^2 + 1.255^2) = 1.340 [m/s]
and the angle is in the second quadrant using tg(angle) = (Vay)/(Vax) you get 102.7 degrees.

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