Question

A stone is dropped from the window of a bus moving at $60\dfrac{{km}}{{hr}}$. If the window is $196cm$ high, what is the distance along the track which the stone moves before striking the ground?

Answer 1

In this question, we need to calculate the distance. So, to calculate distance, we need to have the speed and time. In this question, we are given the speed of the bus. So, in order to find out the distance, we need to first find out the time.

Formula used:
The second equation of motion is $s = ut + \dfrac{1}{2}a{t^2}$. Where,
$s$ is displacement
$u$ is the initial velocity
$a$ is the acceleration
$t$ is the time

Complete step by step answer:
According to the question,
Initial velocity $u = 0\dfrac{m}{s}$
Displacement $s = 196cm$
On converting $s$ in $m$,
$s = \dfrac{{196}}{{100}}m$
$s = 1.96m$
Acceleration $g = 9.8\dfrac{m}{{{s^2}}}$ (as the stone is falling under the action of gravity)
The second equation of motion is,
$s = ut + \dfrac{1}{2}a{t^2}$
On putting the required values, we get,
$1.96 = (0 \times t) + \left( {\dfrac{1}{2} \times 9.8 \times {t^2}} \right)$ $d = 16.67 \times 0.63$
$1.96 = 4.9 \times {t^2}$
On taking $4.9$ on the other side,
${t^2} = \dfrac{{1.96}}{{4.9}}$
${t^2} = 0.4$
On taking square root on both the sides,
$t = 0.63\sec$
Also, we know that,
$v = \dfrac{d}{t}$
$d = v \times t.........(1)$
Now, we have calculated $t = 0.63\sec$
Also, it is given in the question that $v = 60\dfrac{{km}}{h}$
On converting it into $\dfrac{m}{s}$ by multiplying by $\dfrac{5}{{18}}$, we get,
$v = 60 \times \dfrac{5}{{18}}$
$v = 16.67\dfrac{m}{s}$
On putting the value of $v$ and $t$ in equation (1), we get,
$d = 16.67 \times 0.63$
$d = 10.5m$
So, the distance along the track which the stone moves before striking the ground is $d = 10.5m$.

Note: In the question, we are given the value of speed in $\dfrac{{km}}{h}$ and the height of the window in $cm$. So, first we will convert these values in the SI system of units. So, the speed in $\dfrac{{km}}{h}$ will be converted into $\dfrac{m}{s}$ and the height of the window in $cm$ will be converted into $m$.