Question

A ball is dropped from a cliff. Find
(a) its speed $2s$ after it is dropped,
(b) its speed when it has fallen through $78.4m$ , and
(c) the time taken in falling through $78.4m$

Answer 1

Velocity after two seconds

$v=u+gt$

$v=0+9.8\times 2$

$v=19.6m/s$

Velocity when a ball has fallen through $78.4m$ is given by

$v^2-u^2=2gh$

$v^2-0=2\times 9.8\times 78.4$

$v^2=1536.64$

$v=39.2m/s$

Let time taken in falling through $78.4m$ be $ts$.

$h=ut+\frac{1}{2}g{t}^2$

$78.4=0\times t+\frac{1}{2}\times 9.8\times t^2$

$t^2=\frac{78.4}{4.9}$

$t^2=16$

$t=4s$

Thus time taken in falling through $78.4m$ is $4s$.