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 0.130kg apple toward astronaut 2 with a speed of vi,1 = 1.11m/s . The 0.160kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.19m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 1.02m/s in the negative ydirection.

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

Part B) We need to find theta degrees and it is counterclockwise from the positive x axis.

Explanation / Answer

m1 = 0.13 kg

u1 = 1.11 m/s i

m2 = 0.16 kg

u2 = - 1.19 m/s i

v2 = - 1.02 m/s j

Applying conservation of kinetic energy

0.5 m1 u1^2 + 0.5 m2 u2^2 = 0.5 m1 v1^2 + 0.5 m2 v2^2

0.13*1.11^2 + 0.16*1.19^2 = 0.13 v1^2 + 0.16*1.02^2

v1 = sqrt((0.13*1.11^2 + 0.16*1.19^2- 0.16*1.02^2)/0.13) = 1.302 m/s

(a) Final speed of apple = 1.302 m/s

Applying conservation of momentum

m1 u1 + m2 u2 = m1 v1 + m2 v2

0.13 * 1.11 i - 0.16*1.19 i = 0.13* v1 - 0.16*1.02 j

v1 = (0.13 * 1.11 i - 0.16*1.19 i +  0.16*1.02 j ) /0.13

v1 = (- 0.0461 i + 0.16*1.02 j ) / 0.13 = - 0.354 i + 1.255 j

Direction of apple = 180 - arctan(1.255/0.354) = 105.75 0 counterclockwise from the positive x axis

theta =  105.75 0 counterclockwise from the positive x axis

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