- #1
Jam51
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Homework Statement
A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine:
a. the speed of the first ball after the collision.
b. the speed and direction of the second ball after the collision.
Homework Equations
px = p'x (momentum conservation in the x direction)
v1x = v1'cosθ + v2'cosθ
piy = pfy (momentum conservation in the y direction)
0 = v1'sinθ + v2'sinθ
Ki = Kf (conservation of kinetic energy)
v1^2 = v1'^2 + v2'^2
The Attempt at a Solution
I've attempted solving it in a number of values, but am finding the math challenging and unable to isolate variables. First I attempted to eliminate theta:
v1x = v1'cosθ + v2'cosθ
v1x - v1'cosθ = v2'cosθ ---square--
v1x^2 - v1'^2cos^2θ = v2'^2cos^2θ
0 = v1'sinθ + v2'sinθ
-v1'^2sin^2θ = v2'^2sin^2
add x and y
v1x^2 - v1'^2cos^2θ - v1'^2sin^2θ = v2'^2cos^2θ + v2'^2sin^2θ
v1x^2 - v1'^2(cos^2θ + sin^2θ) = v2'^2(cos^2θ + sin^2θ)
v1^2 - v1'^2 = v2'^2
(v1 - v1')(v1 + v1') = v2'^2
Arranging Energy Conservation, v1^2 = v1'^2 + v2'^2 :
v1^2- v1'^2 = v2'^2
(v1 - v1')(v1 + v1') = v2'^2
I feel like I've done something wrong up until this point because everything I get after just doesn't make sense to me. I'm not sure what to equate with what.
Help is greatly appreciated!