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 117 kg, including his armor, hurled himself against a 845-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.53 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:

Explanation / Answer

since this is a elastic collision

both momentum and kinetic energy is conserved

momentum before collision = momentum after collision

(117*u1) + (845*u2) = (117*v1)-(845*v2)

(117*u1)+(845*0) = (-117*v1)+(845*1.53)

117*u1 = (-117*v1)+1292.85..............(1)

kinetic energy before collision = kinetic energy after collision

(0.5*117*u1^2)+(0.5*845*0^2) = (0.5*117*v1^2)+(0.5*845*1.53^2)

(0.5*117*u1^2) = (0.5*117*v1^2) + 989.........(2)

solving (1) and (2) we get

u1 = 6.3 m/sec is the speed before collision

and v1 = 4.76 m/sec is the speed after collision

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