# B How high did my golf ball go? (I have time of flight straight up)

1. May 27, 2017

### applepi38

Years ago, I made a golf ball launcher. It shot straight up at a 90 degree angle. From launch to landing only 2 feet from where it started, it took about 20 seconds before it was back on the ground. Is there a way to determine its maximum speed and height it reached? This has been bugging me for years!

2. May 27, 2017

### Staff: Mentor

It would be easy if we could ignore air resistance: It went up for ten seconds, it went down for ten seconds; maximum upwards speed at the moment that it leaves the launcher is equl to the maximum downward speed as it reaches the ground. Now we just have to calculate how high you have to be to take ten seconds to fall to earth and how fast you're moving when you hit, and $s=at^2/2$ ($s$ is the distance, $a$ is the acceleration from gravity, and $t$ is the time) and a bit of algebra will do that.

In practice the effects of air resistance cannot be ignored. The actual height and final impact speed will lower because of that, but the calculation is appreciably more complicated.

Last edited: May 27, 2017
3. May 28, 2017

### cosmik debris

In addition to what Nugatory said, a golf balls aerodynamics are somewhat complicated I believe.