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.4 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 1.17 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

m1 = mass of skate = 129 kg

m2 = mass of newton = 837 kg

V1i = velocity of skate just before collision

V2i = velocity of newton before collision = 0 m/s

V1f = velocity of skate just after collision

V2f = velocity of newton after collision = 1.17 m/s

Using conservation of momentum

m1 V1i + m2 V2i = m1 V1f + m2 V2f

129 V1i + 837 x 0 = 129 V1f + 837 (1.17)

129 V1i = 129 V1f + 979.3                             eq-1

For perfectly elastic collision

V2f - V1f = V1i - V2i

1.17 - V1f = V1i - 0

V1i = 1.17 - V1f                        eq-2

using eq-1 and eq-2

129 (1.17 - V1f  ) = 129 V1f + 979.3

V1f = - 3.21 m/s

V1i = 1.17 - V1f   = 1.17 - (-3.21) = 2.04 m/s

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