Question

A stone is thrown vertically upwards. It reaches a maximum height in $3\mathrm{s}$. If the acceleration due to gravity be $9.8{\mathrm{ms}}^{-2}$, calculate the initial velocity of the stone.

Answer 1

Step 1: Given data:

Initial velocity = $\mathrm{u}$

Final velocity, $\mathrm{v}=0$

Acceleration, $a=-$Acceleration due to gravity (because the body is thrown upwards and acceleration due to gravity acts downwards).

Thus,$a=-9.8{\mathrm{ms}}^{-2}$

Time, $\mathrm{t}=3\mathrm{s}$

Step 2: Calculating the initial velocity of the stone:

To find out the initial velocity, the first equation of motion is used as,

$\mathrm{v}=\mathrm{u}+\mathrm{at}$

Where Initial velocity = $\mathrm{u}$, Final velocity, $\mathrm{v}=0$, $a=-9.8{\mathrm{ms}}^{-2}$, $\mathrm{t}=3\mathrm{s}$

Putting all the values in equation $\mathrm{v}=\mathrm{u}+\mathrm{at}$

We get,

$$\begin{gathered} 0m/s=\mathrm{u}\mathrm{m}/\mathrm{s}-(9.8m/s^2)\times (3s) \\ 0=\mathrm{u}-29.4 \\ \mathrm{u}=29.4{\mathrm{ms}}^{-1} \end{gathered}$$

Hence, the initial velocity of stone is $29.4{\mathrm{ms}}^{-1}$.