Barron's 2nd Edition DT Q35

Barron's Book

35) This question asks us to find the speed of the roller coaster car at point B in the figure above.

We are given that the car starts at rest at the top of a 25-meter hill. The problem doesn’t mention anything about friction, so we can assume there is no heat energy dissipated. For this problem, we can use the conservation of energy to quickly solve for the speed at the bottom. Let’s start by setting up the conservation of energy.

Where M is mechanical energy, K is kinetic energy, U is potential energy, m is mass, v is speed, g( ≈ 10 m/s^2) is acceleration due to gravity, and h is height

We can see from the equation that we need to find the initial velocity and the initial and final heights in order to solve for the final velocity. We can label the diagram to make it clear which value corresponds to each of the variables.

Now we can plug in the values and solve for the final velocity at point B.

Where m is mass, v is speed, g( ≈ 10 m/s^2) is acceleration due to gravity, and h is height

Answer: B