A sled slides without friction down a small, ice-covered hill.If the sled starts

Question

A sled slides without friction down a small, ice-covered hill.If the sled starts from rest at the top of the hill, its speed atthe bottom is 9.00 m/s. (a) On a second run, the sled starts with a speed of2.00 m/s at the top. When it reaches thebottom of the hill, is its speed 11.0 m/s, more than 11.0 m/s, orless than 11.0 m/s? (b) Find the speed of the sled at the bottom of the hill afterthe second run. A sled slides without friction down a small, ice-covered hill.If the sled starts from rest at the top of the hill, its speed atthe bottom is 9.00 m/s. (a) On a second run, the sled starts with a speed of2.00 m/s at the top. When it reaches thebottom of the hill, is its speed 11.0 m/s, more than 11.0 m/s, orless than 11.0 m/s? (b) Find the speed of the sled at the bottom of the hill afterthe second run.

Explanation / Answer

Given that the speed of sled at bottom is v = 9.00 m/s    --------------------------------------------------------- From the conservation of energy at top and bottom ofthe incline                 mgh = (1/2)mv2                      h = v2 /2g                            = 4.13 m Let initial speed of the sled at height h is u = 2.00m/s From the conservation of energy at top and bottom ofthe incline                 mgh + (1/2)mu2 = (1/2)mv2                                                   v = ( 2gh + u2 )1/2                                       = 9.21 m/s this is less than 10.0 m/s

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