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 0.425 kg ball that is traveling horizontally at 12.0 m/s . Your mass is 68.0 kg . a. If you catch the ball, with what speed do you and the ball move afterwards?b. If the ball hits you and bounces off your chest, so afterwards it is moving horizontally at 9.00 m/s in the opposite direction, what is your speed after the collision?

Answer 1

Explanation:

Given that,

Mass of ball, m = 0.425 kg

Initial speed of the ball, u = 12 m/s

Initial speed of a person, u' = 0

Mass of a person, m' = 68 kg

(a) Let V is the combined speed of the person and the ball. Using conservation of momentum as :

$mu+m'u'=(m+m')V\\\\V=\dfrac{mu+m'u'}{(m+m')}\\\\V=\dfrac{0.425\times 12+0}{(0.425+68)}\\\\V=0.0745\ m/s$

(b) If the ball hits the person and bounces off his chest, so afterwards it is moving horizontally at 9.00 m/s in the opposite direction,. Let v' is the speed of the person after the collision. So,

$mu+m'u'=mv+m'v'$

v = -9 m/s

$mu=mv+m'v'\\\\v'=\dfrac{m(u-v)}{m'}\\\\v'=\dfrac{0.427\times (12-(-9))}{68}\\\\v'=0.131\ m/s$

Hence, this is the required solution.