Question

hOlaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of mass 0.400 kg that is traveling horizontally at 11.1 m/s . Olaf's mass is 74.7 kg

A) If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward? Express your answer numerically in meters per second.

B) If the ball hits Olaf and bounces off his chest horizontally at 7.80 m/s in the opposite direction, what is his speed vf after the collision? Express your answer numerically in meters per second.

Answer 1

first

You are initially at rest.Your initial velocity is zero.Hence your initial momentum p(i) is zero

Mass of ball 'm' = 0.400 kg

velocity of the ball 'u' =11.1 m/s

Initial momentum of ball p!(i)=mu=0.400*11.1 = 4.44 kgm/s

Total initial momentum of you and ball system=p(i)+p!(i)=4.44 kgm/s
Your mass M=74.7 kg

your speed after you catch the ball v = ?

Total final momentum of you and ball system p(f) =(M+m)v=(74.7 + 0.4)v=75.1v

As no external force has acted, the total momentum remains conserved

Total final momentum of you and ball system = Total initial momentum of you and ball system

75.1 v= 4.44

v =4.44 /75.1 = 0.05912 m/s

You and ball move forward with speed 0.05912 m/s

b)

as ball moves in opposite direction its final velocity will have negative sign, v = - 7.8 m/s

Final momentum of the ball = mu = 0.4 * [ - 7.8]= - 3.12 kgm/s

Your final momentum = MV = 74.7V

Total final momentum of you and ball p(f) = 74.7V + (-3.12)

As no external force has acted, the total momentum remains conserved

Total final momentum of you and ball system = Total initial momentum of you and ball system

74.7V + (-3.12) = 4.44

74.7V = 4.44 + 3.12 = 7.56

V = 7.56 / 74.7 = 0.1012 m/s