You are standing on a sheet of ice that covers the football stadium parking lot

Question

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a ball of mass 0.400 kg that is traveling horizontally at 11.0 m/s. Your mass is 70.0 kg.

1)If you catch the ball, with what speed do you and the ball move afterwards?

2)If the ball hits you and bounces off your chest, so afterwards it is moving horizontally at 7.50 m/s in the opposite direction, what is your speed after the collision?

I worked this problem out and wanted some help in finding the right answer, thank you.

Explanation / Answer

1) Conservation of momentum demands pf = p0 This is just mfvf = m0v0 We can solve this for vf by dividing both sides by mf: vf = m0v0 / mf We are given that the ball has a mass of 0.4 kg and a velocity of10 m/s and that you have a mass of 70 kg and are initially at rest,so the ball system has an initial momentum of p0 = p ball = (0.4 kg)(11 m/s) = 4.4 kgm/s When you catch the ball (an ineleastic collision), you have a new mass of mf = 70 kg + 0.4 kg = 70.4 kg Then inserting these values into our expression for vf we have vf = (4.4 kgm/s) / (70.4 kg) = 0.0625 m/s 2) Again we use conservation of momentum. The ball and you still have an intial momentum of p0 = pball = (0.4 kg)(11 m/s) = 4.4 kgm/s After the ball bounces off of you, it has a velocity of 7.50 m/s inthe opposite direction pballf = (0.4 kg)(-7.50 m/s) = -3 kgm/s and you will have a final momentum of m you* v you(f) Conservation of momentum demands p0 = pballf +m you*v you(f) We can solve this for vyouf by subtractingpballf and dividing by m you: v you(f) = (p0 - pballf) /m you Inserting our values, we have vyouf = (4.4 kgm/s + 3 kgm/s) / 70 kg = 0.106 m/s

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