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 119 kg, including his armor, hurled himself against a 893-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.03 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:             After:

Explanation / Answer

Let before collision speed be u m/s

After collision speed be v m/s.

Conservation of momentum gives,

119*u = 893*1.03-119*v

u+v = 7.73 -----------------(1)

Conservation of kinetic energy gives,

(1/2)*119*u2 = (1/2)*119*v2 +(1/2)*893*1.032

u2 - v2 = 7.96------------------(2)

(u+v)*(u-v) = 7.96

(u-v)*7.73 = 7.96

u-v = 1.03 ------------------(3)

From (1) and (3)

u = 4.38 m/s

v = 3.35 m/s

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