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 figure below. The orange puck is initially moving to the right at voi = 5.95 m/s, strikes the initially stationary blue puck, and moves off in a direction that makes an angle of ? = 37.0° with the horizontal axis while the blue puck makes an angle of ? = 53.0° with this axis as in figure (b). Note that for an elastic collision of two equal masses, the separation angle ? + ? = 90.0°. Determine the speed of each puck after the collision.

v0f = _______ m/s

vbf = _______ m/s

Explanation / Answer

By law of conservation of momentum

Pi = Pf

mv0i = m* v0f + m* vbf

v0i = v0f + vbf

Along x axis it becomes,

v0ix = v0fx + vbf x

v0ix = v0f*cos37 + vbf *cos(-53)

5.95 = v0f*cos37 + vbf *cos(-53) -------------(1)

Along y axis it becomes,

v0iy = v0fy + vbfy

v0ix = v0f*sin37 + vbf *sin(-53)

0 = v0f*sin37 - vbf *sin53

v0f*sin37 - vbf *sin53

v0f*sin37 = vbf *sin53

v0f = vbf *(sin53/sin37) -------------(2)

Plugging (2) in (1),

5.95 = [vbf *(sin53/sin37)]*cos37 + vbf *cos(-53)

Gives,    vbf = 3.58 m/s

Plugging this value in (2),

v0f = 3.58 *(sin53/sin37) = 4.75 m/s

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