Question

Nate the Skate was an avid physics student whose main non-physics interest in life was high-speed skateboarding. In particular, Nate would often don a protective suitof Bounce-Tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. In this way, he got a gut feel for the physicalproperties of collisions and succeeded in combining his two passions.* On one occasion, the Skate, with a mass of 129 kg, including his armor, hurled himself against a821-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.35 m/s and Nate bounced backward. What wereNate's speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground. Before:

Answer 1

let,

mass of the skate m1=111 kg

mass of the statue m2=871 kg

initial speed of m1 is u1 and final speed is v1

initial speed of m2 is u2=0 and final speed is v2=1.43 m/sec

by using law of conservation momentum,

m1*u1+m2*u2=m1*v1+m2*v2

111*u1+0=111*v1+871*1.43

111*u1=111*v1+1245.53 ------(1)

and

here, collisoin is perfectly elastic,

coefficient of restitution e=(v2-v1)/(u2-u1)=1

===>

u1-u2=v2-v1

u1-0=1.43-v1

u1=1.43-v1 --------(2)

from (1) and (2)

====> u1=6.32 m/sec and v1=-4.89 m/sec

skate's initial speed u1=6.32 m/sec ( before collision)

skate's final speed v1=4.89 m/sec ( after collision)