# What is the maximum height above the ground for a the gymnast jumping straight upward with initial speed of 10 m/s?

Nov 14, 2017

OK, if we assume that the velocity is positive, the acceleration must be negative (they’re both vectors and they point in opposite directions) .... good to go!

#### Explanation:

We normally start these questions by drawing out a little table with the 5 factors (s, u, v, a, t) listed and all the ones you know written in beside them, with the correct units. This helps you to select the correct equation to use, because it shows which factor is completely irrelevant (and one factor is missing from each kinematic equation.)

Assuming we have done that and chosen ${v}^{2} = {u}^{2} + 2 a s$ we can put in our values, remembering that the final velocity, v is zero (at the top of the jump) and that acceleration will be negative. We should also rearrange the equation to make the unknown (s) the subject:

$s = \frac{{v}^{2} - {u}^{2}}{2 a}$

OK. Next, substitute your numbers in:

$s = \frac{0 - {10}^{2}}{2 \times - 10}$

$s = \frac{- 100}{-} 20$

$s = + 5$ m

So the gymnast travels 5m upwards.