# Boy Scouts are firing model rockets in a field. One boy used a radar gun to determine his rocket had a lift-off velocity of 34 m/s. How high did the rocket travel?

Apr 4, 2018

Assuming that the rocket had a vertical lift-off velocity the applicable kinematic expression is

${v}^{2} - {u}^{2} = 2 g h$
where $v$ is final velocity, $u$ is initial velocity, $g = 9.81 \setminus m {s}^{-} 2$ acceleration due to gravity and $h$ is height of rocket

At maximum height the velocity of rocket will be zero. Noting that $g$ acts against direction of initial motion, inserting various values we get

${\left(0\right)}^{2} - {\left(34\right)}^{2} = 2 \left(- 9.81\right) {h}_{\max}$
$\implies {h}_{\max} = {\left(34\right)}^{2} / \left(2 \times 9.81\right)$
$\implies {h}_{\max} = 58.92 \setminus m$