We drop a 60 gram tennis ball from the top of the Burj Khalifa (828 m).
How fast will it hit the ground if there's no air resistance?
How fast will it hit the ground if the air resistance takes away 200 Joules of energy?
How high will it bounce back if the energy lost during the bounce is 50 Joules?
Calculate the ratio of the output energy vs the input
energy (the efficiency)

50 mph

Explanation:

The very top of the Burj Khalifa is a spire. If you were simply to fall from the top of that spire, the simple answer is that you wouldn't hit the ground, because you would actually hit one of the tower's many terraces before that point. Also, as you wouldn't be able to take a running jump off the top, you'd probably still hit a terrace on the way down even if you leapt from the top.

But let's say that you decide to throw a baseball from the top of the Burj Khalifa instead - if you've made it to the top of that spire, there's really no way you're going to be incapable of throwing a baseball decently far. Let's also assume that you manage to throw that baseball straight, not going upwards in the slightest.

The Burj Khalifa is 829.8 m tall. Tack on another 1.5 meters for the height from your feet to your arms, and that gets us to 831.3 m. Because of the small scale of the drop, we don't have to worry about gravitational acceleration being different between the top of the Burj Khalifa and at the bottom, so we're looking at a constant 9.81 m/s/s.[1] Thus, using physics, we know that the time, t, an object starting at rest and experiencing constant acceleration, g, takes to travel distance y is:

\sqrt{2y/g}

Explanation: