# Please explain to me how to solve this problem: A sledder starts from rest atop a 5.0-m high hill (A). She sleds to the bottom and up to the. . . top of the adjacent 3.0-m high hill. How fast is...

Please explain to me how to solve this problem: A sledder starts from rest atop a 5.0-m high hill (A). She sleds to the bottom and up to the. . .

top of the adjacent 3.0-m high hill. How fast is the sledder going at point B? Ignore friction.

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### 1 Answer

You can solve this problem using conservation of energy; i.e., the total energy in the system is constant.

You are at the top of a hill of 5 m height. As you go down to 3 meters your potential energy decreases and your kinetic energy increases. Since you are ignoring friction, your speed when you have gone down 2 meters is the same as your speed at the top of the 3 meter hill.

At the top of the hill your have PE = mgh, where h = 5

At a point 2 meters lower you have a PE of mgh, where h = 3 + KE = 1/2 mv^2

Since total energy is conserved, you know that:

PE @ the top = PE + KE when you are 2 meters lower.

So:

mg*5 = mg*3 + 1/2 mv^2

divide by m and you get:

5g = 3g+ 1/2v^2

Enter value for g: 9.8 m/s/s and you get

49 = 29.4 + 1/2 v^2

solve for v:

v = 6.26 m/s

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