Two ice pucks (one orange and one blue) of equal mass are involved in a perfectl

Question

Two ice pucks (one orange and one blue) of equal mass are involved in a perfectly elastic glancing collision as shown in the figures below. The orange puck is initially moving to the right at voi = 7.35 m/s, strikes the initially stationary blue puck, and moves off in a direction that makes an angle of ? = 38.0° with the horizontal axis while the blue puck makes an angle of ? = 52.0° with this axis as in the second figure. Note that for an elastic collision of two equal masses, the separation angle ? + ? = 90.0°. Determine the speed of each puck after the collision in meters per second.

Explanation / Answer

let m is the mass of each puck

and v1 and v2 are the speeds of orange puck and blue puck.

apply conservation of momentum in x-direction

m*voi = m*v1*cos(38) + m*v2*cos(52)

7.35 = v1*cos(38) + v2*cos(52)

7.35 = 0.788*v1 + 0.6157*v2 ----(1)

Apply conservation of momentum in y-direction

0 = m*v1*sin(38) - m*v2*sin(52)

v2 = v1*sin(38)/sin(52)

v2 = 0.781*v1 ----(2)

substitute v2 in equation 1

7.35 = 0.788*v1 + 0.6157*0.781*v1

==> v1 = 7.35/(0.788 + 0.6157*0.781)

= 5.79 m/s <<<<<<<<------------Answer

from equation 2

v2 = 0.781*5.79

= 4.52 m/s <<<<<<<<------------Answer

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