In this collision, we need to identify the quantities that are conserved.

In a perfectly elastic collision, both momentum and kinetic energy are conserved.

Conservation of momentum:

$\overline{){{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{v}}}_{\mathbf{0}\mathbf{,}\mathbf{1}}{\mathbf{+}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{v}}}_{\mathbf{0}\mathbf{,}\mathbf{2}}{\mathbf{=}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{,}\mathbf{1}}{\mathbf{+}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{,}\mathbf{2}}}$

Conservation of kinetic energy:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{\left(}}{{\mathbf{v}}}_{{\mathbf{01}}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{\left(}}{{\mathbf{v}}}_{{\mathbf{02}}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{\left(}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{1}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{\left(}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{2}}{\mathbf{\right)}}}^{{\mathbf{2}}}}$

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 801-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.89 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.

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