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 0.120 kg apple toward astronaut 2 with a speed of vi,1 = 1.10 m/s . The 0.170 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 0.927 m/s in the negative y direction.

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

B. What are the degrees counterclockwise from the positive x axis?

Answer 1

In the x direction the initial momentum is

(.12)(1.10) + (0.170)(-1.23) = -0.0771 kg m/s

Since the orange is only in the y direction after this, the apple must take all of the x component, so

-0.0771 = (.12)(v)

vx = - 0.6425 m/s

In the y direction there was no initial momentum, so the apple must counteract the orange, or

(.12)(v) = (0.17)(0.927)

vy = 1.31 m/s

Net velocity is found from the pythagorean theorem

v^2 = (0.64)^2 + (1.31)^2

v = 1.45 m/s

The direction if from the tangent function

tan(angle) = 1.31/.64

angle = 63.88 degrees

Thus the final speed and direction is 1.45 m/s at 63.8 degrees above the negative x axis (or North of West so to speak)

For the angle from the x axis, take the 63.8 and subtract it from 90

90 - 63.8 = 26.12

Now add 90 to 26.1 and get 116.1 degrees from the positive x axis