# Question #beffb

Apr 21, 2017

a) $t = 2 \setminus s$
b) $t = 0 \setminus s$
c) $v = 0 \setminus m {s}^{- 1}$

#### Explanation:

We have height (or displacement) at time $t$, where $h = 0$ is at ground level, and +ve is measured upwards, is given by:

$h \left(t\right) = - 4.9 {t}^{2} + 9.8 t$

Differentiating wrt $t$ will give us the speed:

$\dot{h} \left(t\right) = - 9.8 t + 9.8$

a) When is the rocket travelling at 9.8 m/s down?

$\dot{h} \left(t\right) = - 9.8$
$\therefore - 9.8 t + 9.8 = - 9.8$
$\therefore - 9.8 t = - 19.6$
$\therefore t = 2 \setminus s$

b) When is the rocket travelling at 9.8m/s up?

$\dot{h} \left(t\right) = 9.8$
$\therefore - 9.8 t + 9.8 = 9.8$
$\therefore - 9.8 t = 0$
$\therefore t = 0 \setminus s$

c) How fast is the rocket travelling after 1 second?

When $t = 1$:

$\dot{h} \left(t\right) = - 9.8 + 9.8$
$\text{ } = 0 \setminus m {s}^{- 1}$