At a county fair, two children ram each other head-on while riding on the bumper

Question

At a county fair, two children ram each other head-on while riding on the bumper cars. Jill and her car, traveling left at 3.50 m/s , have a total mass of 345 kg . Jack and his car, traveling to the right at 2.00 m/s , have a total mass of 260 kg .

A) Assuming the collision to be elastic, determine the speed of Jill and her car after the collision.

B) Determine the direction of the velocity of Jill and her car after the collision (to the left, or the right)

C) Determine the speed of Jack and his car after the collision.

D) Determine the direction of the velocity of Jack and his car after the collision. (to the left, or the right?

Explanation / Answer

let values to the right are taken as positive and values to the elft are taken as negative.

then initial total momentum=345*(-3.5)+260*2=-687.5 kg.m/s

let after collision , speed of Jill is v1 and speed of Jack is v2.

(both v1 and v2 are positive meaning they are in right direction

if one or both of them found to be negative, then they will be pointed towards negative direction)

as the collision is elastic, momentum after collision=momentum before collision

==>345*v1+260*v2=-687.5

==>v1=-0.7536*v2-1.9927...(1)

as the collision is elastic, total energy will be conserved.

hence 0.5*345*3.5^2+0.5*260*2^2=0.5*345*v1^2+0.5*260*v2^2

==>2633.125=172.5*(-0.7536*v2-1.9927)^2+130*v2^2

==>2633.125=172.5*(0.5679*v2^2+3*v2+3.97085)+130*v2^2

==>97.9627*v2^2+517.5*v2+684.972+130*v2^2=2633.125

==>227.9627*v2^2+517.5*v2-1948.153=0

solving for v2, we get

v2=2 m/s or v2=-4.271 m/s

if v2=2 m/s, v1=-0.7536*v2-1.9927=-1.5 m/s

that means jill will be moving to the left and jack will be moving to the right

but that is not possible after collision

hence the correct solution is v2=-4.271 m/s

and v1=-0.7536*v2-1.9927=1.226 m/s

answers:

part a: speed of Jill after collison=v1=1.226 m/s

part b: Jill will be moving towards right direction

part c: speed of Jack is 4.271 m/s

part d: Jack will be moving towards left direction

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