A young 35kg ice hockey goalie, originally at rest, catches a 0.135 kg hockey pu

Question

A young 35kg ice hockey goalie, originally at rest, catches a 0.135 kg hockey puck slapped at him at a speed of 35.5 m/s. In this problem take the original direction of the puck as positive.

1) Suppose the goalie and the ice puck have an elastic collision and the puck is reflected back in the direction from which it came. What would the final velocity of the puck , in meters per second, be in this case?

2) Suppose the goalie and the ice puck have an elastic collision and the puck is relgected back in the direction from which it came. What would the final velocity, in meters per second, of the goalie be in this case.

Please show all work and use the elastic collision formulas to solve this problem, this is driving me crazy and I can not figure out how to do this problem. Thanks for your help in advace.

Explanation / Answer

In a perfectly elastic collision

Using momentum conservation

Pi = Pf

m1V1i + m2V2i = m1V1f + m2*V2f

given that m1 = 0.135 kg & m2 = 35 kg

V1i = 35.5 m/sec

V2i = 0

0.135*35.5 + 0 = 0.135*V1f + 35*V2f = 4.7925

Now other condition of the elastic collisions is that

V1f - V2f = V2i - V1i

V1f - V2f = 0 - 35.5

V1f - V2f = -35.5

0.135*V1f + 35*V2f = 4.7925?

Now Solving both equation

Multiply equation 1 with 35 and Add both of them

35.135*V1f = (-35.5*35 + 4.7925)

V1f = (-35.5*35 + 4.7925)/35.135 = -35.227 m/sec

V1f = -35.227 m/sec (-ve sign means ball is reflected backward)

V2f = V1f + 35.5

V2f = -35.227 + 35.5 = 0.273 m/sec

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