Please solve a$),$ b$),$ c$),$ d$),$ thank you.

When a steel ball having mass $m$ and radius $R$ is dropped against a steel table, Hertzian contact theory

predicts the following quantities:

duration of contact:

$t_C=2\mathrm{.}87(\frac{m^2}{E^{**2}Rv}{)}^{\frac{1}{5}}$

maximum contact force during contact:

$F_{\text{m}\text{a}\text{x}}=\frac{4}{3}{E}^{**}\sqrt[\phantom{2}]{R}(\frac{15m{v}^2}{16E^{**}\sqrt[\phantom{2}]{R}}{)}^{\frac{3}{5}}$

maximum radius of contact circle: $,a=(\frac{3F_{\text{m}\text{a}\text{x}}R}{4E^{**}}{)}^{\frac{2}{3}}$

maximum ball compression: $,=\frac{a^2}{R}$

where

$v$ is the speed of the ball just before impact

$E^{**}=\frac{E}{2(1-v^2)}$

and

$E$ is the modulus of elasticity of steel, $v$ is the Poisson's ratio of steel.

Suppose a steel ball, having a radius of $1\mathrm{.}25$ cm is dropped from a height whereby it descends $1\mathrm{.}0$ m before

hitting the surface of a steel table. Assuming a purely elastic collision, find, for the impact:

a$)$ the average contact force

b$)$ the maximum contact force

c$)$ the maximum ball compression

d$)$ the maximum contact pressure