Answer
(a) $1.54\times 10^6m$
(b) $5.51Km/s$
Work Step by Step
(a) We can find the required height as follows:
First of all, we convert calories into joules
$Q=525cal(\frac{4186J}{cal})=2.20MJ$
Given that $Q=P.E$
$\implies Q=mgh$
This can be rearranged as:
$h=\frac{Q}{mg}$
We plug in the known values to obtain:
$h=\frac{2.198\times 10^6}{(0.145)(9.81)}$
$h=1.54\times 10^6m$
(b) We can find the required speed as follows:
$\frac{1}{2}mv^2=Q$
This simplifies to:
$v=\sqrt{\frac{2Q}{m}}$
We plug in the known values to obtain:
$v=\sqrt{\frac{2(2.198\times 10^6)}{0.145}}$
$v=5.51Km/s$
