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 129 kg, including his armor, hurled himself against an 831 kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.29 m/s and Nate bounced backward. What were Nate's speeds immediately before and after the collision? Ignore friction with the ground. Choose the correct option;
(a) before collision: 4.8m/sAfter Collision: 1.29m/s
(b) before collision: 2.8m/sAfter Collision: 2.29m/s
(c) before collision: 3.8m/sAfter Collision: 3.29m/s
(d) before collision: 5.8m/sAfter Collision: 1.29m/s

Answer 1

Answer:

$v_{1i} = 4.8 m/s$

$v_{1f} = 3.51 m/s$

Explanation:

Since the collision is perfectly elastic collision so here we can use momentum conservation

$m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$

so we will have

$129 v_{1i} + 0 = 129(-v_{1f}) + 831(1.29)$

$v_{1i} + v_{1f} = 8.31$

also by elastic collision property we will have

$1.29 + v_{1f} = v_{1i}$

now from above two equations we have

$v_{1i} = 4.8 m/s$

$v_{1f} = 3.51 m/s$