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 131 kg, including his armor, hurled himself against a 877-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.05 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

according to law of conservation of kinetic energy

0.5*Ma*Va^2 + 0.5*Mb*Vb^2 = 0.5*Ma*Va'^2+ 0.5*Mb*Vb'^2

Ma*(Va^2Va'^2) = Mb*(Vb'^2-Vb^2)


solving the above two equation
we get
velocity after collision

Va' = (Ma-Mb)*Va/(Ma+Mb) + 2*Mb*Vb /(Ma+Mb)............(3)

Vb' = (Mb-Ma)*Vb/(Ma+Mb) + 2*Ma*Va /(Ma+Mb)..........(4)


Vb' = 1.05 m/s

1.05 = 0 + 2*131*Va/(131+877)

Va = 4.039 m/s

Va' = (131-877)*4.039/(131+877) + 0
Va' = ?2.989 m/s

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