Please Help!!! Two astronauts on opposite ends of a spaceship are comparing lunc

Question

Please Help!!!

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 0.125 kg apple toward astronaut 2 with a speed of vi,1 = 1.09 m/s . The 0.150 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.22 m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 1.04 m/s in the negative y direction. What are the final speed and direction of the apple in this case?

Explanation / Answer

here,

mass of orange , m1 = 0.15 kg

u1 = - 1.22 m/s i

mass of apple , m2 = 0.125 kg

u2 = 1.09 m/s i

final speed of orange , v1 = - 1.04 m/s j

let the speed of apple be v2 in direction theta

using conservation of momentum in x axis

m1u1 + m2u2 = m1u1 + m2u2

- 0.15 * 1.22 i + 0.125 * 1.09 i = 0.125 * v2*cos(theta)

v2 * cos(theta) = - 0.04675 ....(1)

using conservation of momentum along y axis

0 = m1*v1 + m2*v2* sin(theta)

v2*sin(theta) = 1.248 ......(2)

from equation (1) and (2)

theta = 87.85 degree

v1 = 1.25 m/s

the final speed and direction of the apple is 1.25 m/s and 92.15 degree counterclockwise from + x axis

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