Answer
(a) Use $\frac{1}{2}mv_i^2=mgh_f$ to find g and use $g=\frac{GM}{R^2}$ to find M.
(b) $8.94\times 10^{22}Kg$
Work Step by Step
(a) We can find 'g' from this equation $\frac{1}{2}mv_i^2=mgh_f$ and then we can use $g=\frac{GM}{R^2}$ to find the required mass M.
(b) We know that
$\frac{1}{2}mv_i^2=mgh_f$
This can be rearranged as:
$g=\frac{v_i^2}{2h_f}$
We plug in the known values to obtain:
$g=\frac{(134m/s)^2}{2(5.00\times 10^3m)}$
$g=1.80m/s^2$
Now we can find the required mass as
$M=\frac{gR^2}{G}$
We plug in the known values to obtain:
$M==\frac{(1.80m/s^2)(1.82\times 10^6m)^2}{6.67\times 10^{-11}N.m^2/Kg^2}$
$M=8.94\times 10^{22}Kg$
