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 .13kg apple towards astronaut 2 with a speed of 1.11 m/s. The .16kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.21 m/s. Unfortunately the fruits collide, sending the orange off with a speed of 1.16 m/s at an angle of 42degrees. find the speed and direction of the apple, assuming an elastic collision. Please solve using conservation of momentum.

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Asked Oct 25, 2019
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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 .13kg apple towards astronaut 2 with a speed of 1.11 m/s. The .16kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.21 m/s. Unfortunately the fruits collide, sending the orange off with a speed of 1.16 m/s at an angle of 42degrees. find the speed and direction of the apple, assuming an elastic collision. Please solve using conservation of momentum.

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Expert Answer

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Step 1

Consider that the line connecting them as x-axis and perpendicular to it as y-axis. Also, assume that direction from 1 to 2 is positive and 2 to 1 is negative.

Final velocity of the orange along x and y direction is:

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=-(1.16 m/s)cos 42 (1.16 m/s)sin 420 orange orange

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Step 2

Apply the conservation of momentum along x-direction.

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m fiApple m 'orange 'orange (Vix )erange = mApple orange т, 1Appie (Va )appie ((0.13 kg)(v4)4pie ((0.13 kg)(1.11 m/s) +(0.16 kg)(-1.21 m/s)(0.16 kg) (-(1.16 m/s ) cos 42°) (0.16 kg)(1.21 m/s) (1.11 m/s) 0.13 kg (vA) Apple +(0.16 kg)(1.16 m/s) cos 42°) 0.6818 m/s

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Step 3

Apply the conservation of mome...

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(,) m orange Аpple т Apple = m Apple orange Apple orange orange ((0.13 kg)(spte Apple (0.13 kg) (0 m/s)+(0.16 kg)(0 m/s)= +(0.16 kg) ((1.16 m/s) sin 42°) 0.16 kg1.16 m/s )sin 42°) 0.13 kg Аple =-0.9553 m/s

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Science

Physics

Collisions