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 129 kg, including his armor, hurled himself against a 837-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.97 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

Mass of Skate M1 = 129 kg

Mass Of Isaac M2 = 837 kg

Initial velocity of Isaac V2i =0

Final velocity of Statue V2f = 1.97 m/s

We can use momentum conservation equation

M1V1i + M2V2i = M1V1f +M2V2f

129*V1i + 0 = 129 V1f + 837(1.97)

129*V1i = 129 V1f + 1648.89

Now we can use

velocity of separation = velocity of appraoch

V1i - V2i = V2f - V1f

V1i - 0 = 1.97 - V1f

V1i = 1.97 - V1f

We can plug this in first equation

129*(1.97 - V1f) = 129 V1f + 1648.89

254.13 - 1648.89 = 258 V1f

V1f = - 5.41 m/s

V1i = 1.97 - V1f

V1i = 7.38 m/s

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