Two astronauts on opposite ends of a space ship are comparing lunches. One has a

Question

Two astronauts on opposite ends of a space ship are comparing lunches. One has an apple, the other has an orange. They decide to trade. Astronaut 1 tosses the 0.160-kg apple toward astronaut 2 with a speed of 1.23 m/s. The 0.130-kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.12 m/s. Suppose that after the collision the orange moves exactly in the negative y direction with a speed of 1.26 m/s (not at the angle drawn in the figure). What is the final speed and direction of the apple in this case?

vf =  m/s ? =   Two astronauts on opposite ends of a space ship are comparing lunches. One has an apple, the other has an orange. They decide to trade. Astronaut 1 tosses the 0.160-kg apple toward astronaut 2 with a speed of 1.23 m/s. The 0.130-kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.12 m/s. Suppose that after the collision the orange moves exactly in the negative y direction with a speed of 1.26 m/s (not at the angle drawn in the figure). What is the final speed and direction of the apple in this case? vf = m/s ? = degree (counterclockwise from the positive x axis)

Explanation / Answer

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Two astronauts on opposite ends of a space ship are comparing lunches. One has an apple, the other has an orange. They decide to trade. Astronaut 1 tosses the 0.160-kg apple toward astronaut 2 with a speed of 1.22 m/s. The 0.130-kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.10 m/s. Suppose that after the collision the orange moves exactly in the negative y direction with a speed of 1.23 m/s . What is the final speed and direction (counterclockwise from the positive x axis) of the apple in this case?

From conservation of momentum (p)we have

y -dir pi = 0 = pf So the momenta of the fruit in the y direction must be equal and opposite

So ma*vay = mo*voy (a - apple o orange)

vay = mo*moy/ma = 0.130*1.23/.160 = 0.999m/s ( + y)

x - dir 0.160*1.22 - 0.130*1.10 = mo*0 + ma*vax

So vax = (.160*1.22 -.130*1.10)/.160 = 0.326m/s

So va = sqrt(.999^2 + .326^2) = 1.05m/s

theta = arctan(.999/.326) = 71.9o

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