Answer
The correct answer is: (b) $6h$
Work Step by Step
We can assume that the kangaroo's initial vertical velocity $v_{0y}$ is the same on the Earth and on the moon.
We can find an expression for the kangaroo's height on Earth:
$v_{yf}^2 = v_{0y}^2+2a_yh$
$h = \frac{v_{yf}^2 - v_{0y}^2}{2a_y}$
$h = \frac{0 - v_{0y}^2}{(2)(-g)}$
$h = \frac{v_{0y}^2}{2g}$
We can find an expression for the kangaroo's height on the moon:
$v_{yf}^2 = v_{0y}^2+2a_yh_m$
$h_m = \frac{v_{yf}^2 - v_{0y}^2}{2a_y}$
$h_m = \frac{0 - v_{0y}^2}{(2)(-g/6)}$
$h_m = 6\times\frac{v_{0y}^2}{2g}$
$h_m = 6h$
The correct answer is: (b) $6h$
