Question

A ball is thrown vertically upwards from the ground with a speed of $36km/h$.
If $g$ is approximately $10m/s^2$, then the maximum height attained by the ball and the time taken to attain it are ____ and ____, respectively.

• A. $5m$, $1s$
• B. $5m$, $0.5s$
• C. $6m$, $1s$
• D. $6m$, $0.5s$

Answer 1

The correct option is A $5m$, $1s$

The initial velocity of the ball is,
$u=36km/h$ or $10m/s$

At the maximum height, the velocity of the ball will reduce to zero, i.e., v = 0.

The direction of motion of the ball and the direction of acceleration due to gravity are opposite. So, the sign of acceleration due to gravity $\left(g\right)$ will be taken as negative in both the equations.

Then, by the first equation of motion,
$\Rightarrow v=u+at$
$\Rightarrow v=u-gt$
$\Rightarrow 0=10-gt$
$\Rightarrow t=1s$

The maximum height attained by the ball in $1s$ can be determined using the second equation of motion.
$\Rightarrow s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow s=ut-\frac{1}{2}g{t}^2$
$\Rightarrow s=(10\times 1)-\frac{1}{2}\times \left(10\right)\times \left(1^2\right)$
$\Rightarrow s=5m$

Thus, the maximum height attained by the ball and the time taken to attain it are $5m$ and $1s$, respectively.

Therefore, option A is correct.