Two astronauts on opposite ends of a spaceship are comparing lunches. One has an
ID: 2143751 • Letter: T
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 = 1.08m/s. The 0.150kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.24m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 1.06m/s in the negative y direction.
A) What are the final speed and direction of apple in this case??
Can someone walk me through this STEP BY STEP! I don't know how to set up the coordinate system involving the x and y components and I get confused in the masses and velocities.
Explanation / Answer
Using conservation of momentum:
Before:
x direction: 0.130*1.08 - 0.150 * 1.24 =-0.0456 [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 =-0.0456(momentum did not change) hence:
Vax = -0.35076923076 [m/s]
y direction: 0.130 * Vay -0.150 * 1.06= 0 hence Vay = 1.22307692308 [m/s]
so the apple has a speed of sqrt( (-0.3507)^2 + 1.22307692308^2) = 1.27236301807[m/s]
= (Vay)/(Vax) you get -73.9995500871degrees