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 0.380 kg ball that is traveling horizontally at 12.0 m/s . Your mass is 65.5 kg . Part A) If you catch the ball, with what speed do you and the ball move afterwards? Part B) If the ball hits you and bounces off your chest, so that afterwards it is moving horizontally at 8.05 m/s in the opposite direction, what is your speed after the collision?

Explanation / Answer

Given,

Mb = 0.380 kg ; Ub = 12 m/s ;

My = 65.5 kg ; Uy = 0 m/s

A)Let V be the speed with which you and the ball moves.

The collision here is enelastic. So, From conservation of linear momentum

Mb Ub + My Uy = (Mb + My) V

0.380 x 12 + 0 = (0.38 + 65.5) V

V = 4.56/65.88 = 0.0692 m/s

Hence, V = 0.0692 m/s (aprox V = 0.07 m/s)

B)Vb = - 8.05 m/s ( - since its in opp. direction)

The collision is enelastic. So, From conservation of linear momentum

Pi = Pf

Mb Ub + My Uy = Mb Vb + My Vy

0.38 x 12 = 0.38 x (-8.05) + 65.5 x Vy

Vy = 0.116 m/s

Hence, Vy = 0.116 m/s (Vy = 0.12 m/s aprox.)

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