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 831-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.33 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.

Explanation / Answer

let

m1 = 115 kg

m2 = 831 kg

after the collision,

velcoity of m2, v2 = 1.33 m/s

v1 = ?

before the collsion,

let u1 is the velocity of m1.

u1 = ?

a) v2 = 2*m1*u1/(m1+m2)

==> u1 = v2*(m1+m2)/(2*m1)

= 1.33*(115+831)/(2*115)

= 5.47 m/s speed of skate before the collision.

b) v1 = (m1-m2)*u1/(m2+m2)

= (115 - 831)*5.47/(115+831)

= -4.14 m/s

|v1| = 4.14 speed of skate just after the collision.

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