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 111 kg, including his armor, hurled himself against a 895-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.75 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:

Answer 1

since there is no net external force on system of Nate and statue so momemtum of system just before and after collision will be same .

let's say speed of Nate before collision = u m/s

so momentum of system = 111*u

since it's perfectly elastic collision so no energy loss

now ,

let's final velocity of Nate be V so

1/2 * m * u * u = 1/2 * m * V* V + 1/2 * 895 * 1.75 * 1.75

and

111*u = 895*1.75-111*V

u = 14.1103603604 - V

u+V = 14.1103603604

since

1/2 * m * u * u = 1/2 * m * V* V + 1/2 * 895 * 1.75 * 1.75

u^2 = V^2 +24.6931306306

u^2 = (14.1103603604- u)^2 + 24.6931306306

u^2 = 199.1022695+ u^2 - 28.2207207208* u + 24.6931306306

28.2207207208* u= 223.795400131

u = 7.93018018018 m/s

V =6.18018018022 m/s