Throwing Straight Up

The question

Throw a ball straight up at 15 m/s. How high does it go, and how fast is it when it lands back in your hand?

It rises 11.5 m, which takes 1.53 s, and it lands back in your hand 1.53 s later moving at 15 m/s, now downwards. At the top its velocity is zero for an instant, but its acceleration is still 9.8 m/s² downwards the whole time.

In words, then in symbols

• The highest point is the throwing speed squared divided by twice $g$.

  $h={\displaystyle \frac{u^2}{2g}}$

How to solve a vertical throw

1. Choose up as positive, so the acceleration is $a=-9.8$ m/s².
2. At the highest point, use $v=0$.
3. Pick the equation of motion that holds your unknown.
4. For the way down, use the symmetry: the same time as the way up, and the same speed at the starting height.