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 113 kg, including his armor, hurled himself against a 803-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.55 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

M1×U1 + M2×U2 = M1×V1 + M2×V2 and U1 - U2 = V2 - V1 where M1 = mass 1 = 113 kg M2 = mass 2 = 803 kg U1 = speed of mass 1 before collision = ? U2 = speed of mass 2 before collision = 0 m/s V1 = speed of mass 1 after collision = ? V2 = speed of mass 2 before collision = 1.55 m/s so 113×U1 + 803×0 = 113×V1 + 803×1.55 113×U1 = 113×V1 + 1244.65 . . . . . . . .(equation 1) and U1 - 0 = 1.55 - V1 U1 = 1.55 - V1 . . . . . . . . . . . . . . . . . . (equation 2) substitute (equation 2) in (equation 1) 113×(1.55 - V1) = 113×V1 + 1244.65 175.15 - 113×V1 = 113×V1 + 1244.65 -1069.5 = 226×V1 V1 = - 4.73 m/s substitute that value in (equation 2) U1 = 1.55 - ( - 4.73) U1 = 6.28 m/s Answer: Nate's speed immediately before the collision is 6.28 m/s (forwards) Nate's speed immediately after the collision is 4.73 m/s (backwards)

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