A roller coaster car starts stationary at the top of a downwards slope. At the bottom of the slope, it has a speed of 30m/s. Use the conservation of energy to find the vertical height of the slope. (Use g=10 m/s^2)

From the conservation of energy, we know that the change in gravitational potential energy (GPE) is equal to the change in kinetic energy (KE). GPE=mgh and KE=(1/2)mv^2. At the top of the slope, the car starts stationary so has KE=0 and at the bottom of the slope GPE=0. Therefore the GPE at the top equals the KE at the bottom. mgh=(1/2)mv^2. Divide both sides by the mass (m) to get gh=(1/2)v^2 and rearrange to find h, h=v^2/2g. Substitute in the numbers to find h=45m (don't forget units!)