Answer
$1.04m$
Work Step by Step
We can find the required height as follows:
According to law of conservation of energy
$E_i=E_f$
$\implies U_i+K_i=U_c+k_c$
$\implies mgh+0J=\frac{1}{2}mv_c^2+0J$
This simplifies to:
$v_c=\sqrt{2gh}$
We know that the range is given as
$R=v_c\sqrt{\frac{2h^{\prime}}{g}}$
$\implies R=\sqrt{\frac{2h^{\prime}}{g}}\times \sqrt{2gh}$
$R=\sqrt{\frac{2gh\times 2h^{\prime}}{g}}$
This simplifies to:
$h=\frac{R^2}{4h^{\prime}}$
We plug in the known values to obtain:
$h=\frac{(2.5m)^2}{4\times 1.5m}$
$h=1.04m$
