Nate the Skate was an avid physics student whose main non-physics interest in li

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 suit of 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 physical properties of collisions and succeeded in combining his two passions.* On one occasion, the Skate, with a mass of 115 kg, including his armor, hurled himself against a 805-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.57 m/s and Nate bounced backward. What were Nate's speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground.

Before: ? m/s

After: ? m/s

Explanation / Answer

let,

mass of the nate m1=115 kg

mass of the statue m2=805 kg

initial speed of m1 is u1 and final speed is v1

initial speed of m2 is u2=0 and final speed is v2=1.57

by using law of conservation momentum,

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

115*u1+0=115*v1+805*1.57

115*u1=115*v1+1263.85 ------(1)

and

here, collisin is perfectly elastic,

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

===>

u1-u2=v2-v1

u1-0=1.57-v1

u1=1.57-v1 --------(2)

from (1) and (2)

====> u1=6.28 m/sec and v1=-4.71 m/sec

Nate's initial speed u1=6.28 m/sec ( before collision)

Nate's final speed v1=4.71 m/sec ( after collision)

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