A car going over a cliff

The police find a car at a distance w = 20 m from the base of a cliff of height h = 100 m. How fast was the car going when it went over the edge? Solve the problem symbolically first, then plug in the numbers.

Let's choose y pointing up and x pointing away from the cliff. The car's vertical motion was independent of its horizontal motion, so we know it had a constant vertical acceleration of a = -g = -9.8 m/s². The time it spent in the air is therefore related to the vertical distance it fell by the constant-acceleration equation

or

Solving for Δt gives

Since the vertical force had no effect on the car's horizontal motion, it had ax = 0, i.e., constant horizontal velocity. We can apply the constantvelocity equation

i.e.,

We now substitute for Δt to find

which simplifies to

Plugging in numbers, we find that the car's speed when it went over the edge was 4 m/s, or about 10 mi/hr.