A child\'s sled has rails that slide with little friction across the snow. Logan

Question

A child's sled has rails that slide with little friction across the snow. Logan has an old wooden sled with heavy iron rails that has a mass of 8.0kg quite a bit for a 29kg child! Logan runs at 4.3m/s and leaps onto the stationary sled and holds on tight as it slides forward. The impact time with the sledis 0.27s .

So this is what i got so far
-after the jump the sled is moving 3.4 m/s
-the force on impact is 460N

HELP ON THIS
How much energy was "lost" in the impact?

and where did the energy go
a. kinetic energy.
b gravitational potential energy.
c thermal energy.
d elastic potential energy.

Explanation / Answer

29 x 4.3 = (29 + 8) . V (sled ) V =29 x 4.3 / 37 Force . time = change in momentum of the sled F x 0.27 = 8 x29 x 4.3 / 37 F = 8x 29 x 4.3 / 37 x 0.27 N Energy "lost" is (0.5 x 29 x 4.3^2 ) - ( 0.5 x 37 x ( 29x 4.3 / 37 )^2 ) = 268.105 - 210.136 = 57.968

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