Physics help! Got an answer, don’t know why it’s wrong?

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The sledder shown in the figure below starts from the top of a frictionless hill and slides down into the valley. What initial speed vi does the sledder need to just make it over the next hill? (Height of first hill is 30m, height of second is 42m)So I first found the velocity the sledder will have at the bottom of the hill by setting kinetic energy equal to potential energy and I got 24.25. Then I solved for the energy needed to get from the valley to the top of the second hill by doing the same thing, I got 28.69. I then said that 24.25 + v = 28.69. I solved for v and got 4.44. However, this is wrong. I don't understand why! Help please!

Everardo Feil · Accepted Answer

You don't really want the velocity needed at the bottom. It's energy and not velocity that's conserved. In this case, you don't even need to know the kinetic energy needed at the bottom. All you need is kinetic energy at the start that is equal to the potential energy difference between the two hilltops:(1/2)m(v0)² = mg(42 m - 30 m)v0 = sqrt(2g12 m)which I get as about 15.3 m/s. In the absence of friction, the mg(30 m) work done by gravity on the way down and the -mg(30 m) done on the first 30 m of the way back up cancel out.The reason you got a bad velocity is that velocity doesn't add in this case. Adding 15.3 m/s velocity at the top doesn't add 15.3 m/s at the bottom. Since the sled is already moving, it's average velocity over the 30 m is greater and therefore the time that it is accelerated by gravity is smaller than the starting from rest situation. You worked it out...that 15.3 m/s difference only adds about 4.4 m/s to the speed at the bottom.

Everardo Feil · Answer

It seems to me all you need to do is calculate the velocity attained in a drop equal to (42 - 30) = 12m. If it's all frictionless, shouldn't that be the velocity you need?

Everardo Feil · Answer

KE + PE = Total EnergyThe mass will cancel so we can work with:PE = GHKE = 0.5 V^2PE top of first hill = 9.8 * 30 = 294PE top of second hill = 9.8 * 42 = 411.6===>411.6 - 294 = 117.6 worth of KEKE = 0.5 V^2117.6 = 0.5BV^2V^2 = 235.2V = 15.34 m/s

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Physics help! Got an answer, don’t know why it’s wrong?

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