Sapling Learning Nate the Skate was an avid physics student whose main non-physi

Question

Sapling Learning 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 127 kg, including his armor, hurled himself against a 863-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.63 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 Number m/s After Number m/s "By the way, this brief bio of Nate the Skate is written in the past tense, because not long ago he forgot to put on his Bounce-Tex before colliding with the Washington Monument in a perfectly inelastic collision, We will miss him. Previous 3 Gneup & Viaw solution 2 check Answer 0 Next I Exit

Explanation / Answer

as collision is elastic , both momentum and kinetic energy will be conserved.

let the direction in which Nate is moving before the collision is positive.

let speed (magnitude of velocity) before collision is v1 and after collision is v2.

conserving momentum before and after collision:

momentum of nate before collision + momentum of Newton before collision=momentum of Nate after collision + momentum of newton after collision

==>127*v1+863*0=-127*v2+863*1.63 [ note: -ve sign is used for v2 as Nate bounced back and moved in opposite direction]

==>127*(v1+v2)=1406.7

==>v1+v2=11.076...(1)

conserving kinetic energy before collision and after collision:

0.5*127*v1^2+0.5*863*0^2=0.5*127*v2^2+0.5*863*1.63^2

==>127*(v1^2-v2^2)=2292.9

==>v1^2-v2^2=18.054

==>(v1-v2)*(v1+v2)=18.054

==>v1-v2=18.054/11.076

==>v1-v2=1.63....(2)

adding equation 1 and 2,

2*v1=12.706

==>v1=6.353 m/s

v2=11.076-v1

=4.723 m/s

so speed before collsion is 6.353 m/s

speed after collision is 4.723 m/s.

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