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 0.125 kg apple toward astronaut 2 with a speed of vi,1 = 1.07 m/s . The 0.170 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.20 m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 0.932 m/s in the negative y direction.

Part 1: What are the final speed and direction of the apple in this case?

Explanation / Answer

The initial kinetic energy of the system is

Ki = 1/2 ma vi^2 + 1/2 mo vi^2

= 1/2 (0.125) ( 1.07)^2 + 1/2 ( 0.170)( 1.2)^2

=0.193 J

the final kinetic energy is

Kf = 1/2 ma vf^2 + 1/2 mo vf^2

= 1/2 (0.125) ( vf)^2 + 1/2 ( 0.170)( 0.932)^2

=0.0625 ( vf^2 ) + 0.07383304 J

Ki = Kf

0.193 J=0.0625 ( vf^2 ) + 0.07383304 J

vf = 1.38

since final y component momentum is zero

0=ma v1f sin theta - mo v2f sin 42

sin theta = ( 0.170)( 0.932) sin 42/0.125 ( 1.38)

theta = sin^-1 (  ( 0.170)( 0.932) sin 42/0.125 ( 1.38)

=37.92 degree

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