Question

Object	Acceleration Due to Gravity $\left(m/s^2\right)$
Earth	$9.8$
Moon	$1.6$
Mars	$3.7$
Venus	$9.5$
Jupiter	$24.5$

The approximate height h of an object launched vertically upward after an elapsed time t is represented by the equation $h=-\frac{1}{2}a{t}^2+v_{0}t+h_0$, where $a$ is acceleration due to gravity, $v_0$ is the object's initial velocity, and $h_0$ is the object's initial height. The table above gives the acceleration due to gravity on Earth's moon and several planets. If two identical objects are launched vertically upward at an initial velocity of $40m/s$ from the surfaces of Mars and Earth's moon, approximately how many more seconds will it take for the moon projectile to return to the ground than the Mars projectile?

• A. $21$
• B. $28$
• C. $36$
• D. $50$

Answer 1

Answer: (B)

$28$

We have $h=-\frac{1}{2}a{t}^2+v_{o}t+h_0$
Initial height $=0$, height of the object $=0$.
Initial velocity $=40$m/s
Moon projectile: $0=-\frac{1}{2}\left(1.6\right)t^2+40t$
$\Rightarrow 0.8t^2=40t$
$\Rightarrow t=\frac{40}{0.8}=50$
Mars projectile $=$ $0=-\frac{1}{2}\left(3.7\right)t^2+40t$
$\Rightarrow 1.85t^2=40t$
$\Rightarrow t=\frac{40}{1.85}=21.62$
The approximate seconds will it take for the moon projectile to return to the ground than the Mars projectile $=$ $50-21.62\approx 28$