INSANELY TOUGH QUESTION FOR ME PLEASE HELP, WILL BE COMING IN EXAM FOR SURE A 12

Question

INSANELY TOUGH QUESTION FOR ME PLEASE HELP, WILL BE COMING IN EXAM FOR SURE

A 120g ball moving to the right at 4.2m/s catches up and collides with a 450g ball that is moving to the right at 1.1m/s . If the collision is perfectly elastic, what is the speed of the 120g ball after the collision? Express your answer to two significant figures and include the appropriate units. If the collision is perfectly elastic, what is the direction of motion of the 120g ball after the collision? To the left To the right If the collision is perfectly elastic, what is the speed of the 450g ball after the collision? Express your answer to two significant figures and include the appropriate units. If the collision is perfectly elastic, what is the direction of motion of the 450g ball after the collision? To the left To the right

Explanation / Answer

in elastic collisions, both momentum and energy are conserved

momentum conservation gives us

120g x 4.2m/s + 450g x 1.1m/s = 120v1 + 450v2 where v1 and v2 are the speeds of the masses after collision

we can write the left side as 999gm/s = 120v1 + 450v2 (eq. 1)

energy conservation gives us

1/2 x 120g x (4.2m/s)^2 + 1/2 x 450g (1.1m/s)^2 = 1/2 x 120g v1^2 + 1/2 x 450g v2^2

or 1330.65 = 1/2 x 120g v1^2 + 1/2 450g v2^2

or 1330.65 = 60 v1^2 + 225 v2^2 (eq. 2)

rewrite eq. 1 as (850 - 100v1)/400 =v2

and substitute this expression for v2 into eq. 2

this gives you a quadratic for v1, which you solve for v1, I get v1 = -2.7839 m/s meaning it rebounds

therefore, v2 = (999-120v1)/450 = 2.9623m/s moves forward (to the right)

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