Question

A stone piece is just dropped from a height of $180m$. If its velocity increases uniformly at the rate of $10m/s^2$, with what velocity will it strike the ground? How much time does the stone take to reach the ground?

Answer 1

Step 1: Given

Height, $s=180m$

Initial velocity, $u=0m/s$

Acceleration, $a=10m/s^2$

Step 2: Calculation of time

For uniformly accelerated motion, the velocity-time relation is given by,

$v=u+at.$

To find the time, first, we have to calculate the final velocity by using the relation,

$v^2=u^2+2as$

Step 3: Calculation of final velocity

$v^2={\left(0\right)}^2+2\times 10\times 180$

$v^2=3600m/s.$

$v=60m/s.$

Sep 4: Calculation of time

Using the relation, $v=u+at$.

$60=0+10\times t$

$10t=60$

$t=\frac{60}{10}=6seconds.$

Hence, the time taken by stone to reach the ground is 6 seconds and the stone will reach the ground with a velocity of $60m/s.$