Question

A stone is thrown in a vertically upward direction with a velocity of $5m{s}^{-1}$. If the acceleration of the stone during its motion is $10m{s}^{-2}$ in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

Answer 1

Step 1: Given

Initial velocity (u) = $5m{s}^{-1}$

Acceleration = $-10m{s}^{-2}$

Final velocity (v) = $0$

Step 2: Formula and calculation

$$\begin{gathered} v^2=u^2+2as \\ 0=5^2+2(-10)\times s \\ 20s=25 \\ s=\frac{25}{20} \\ s=1.25m \end{gathered}$$

Hence, the maximum height is $1.25m$.

Now,

$$\begin{gathered} v=u+at \\ 0=5+(-10)t \\ 10t=5 \\ t=\frac{5}{10} \\ t=0.5s \end{gathered}$$

Hence, time taken to reach maximum height is $0.5s$.