Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A roller-coaster car starts from rest above the ground. Ignoring friction and taking , how fast is it moving
When only conservative forces (gravity, springs) do work, mechanical energy is conserved: . Forces that do no work, like a smooth surface's push or a string at right angles to the motion, do not spoil it.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. from the start.
Step 1. (a) : .
Step 2. (b) : .
Answer: (a) . (b) .
Check. The lower point gives the higher speed, as it should.
Watch out. A real car loses energy to friction and air, so a second hill must be lower than the start.
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