Question

A ball is thrown vertically upwards with a speed of $9.8\text{m/s}$ from the top of tower. If it returns to ground in $3\text{seconds}$, find the height of tower. (Take $g=9.8{\text{m/s}}^2$)

• A. $58.6\text{m}$
• B. $14.7\text{m}$
• C. $18.9\text{m}$
• D. $24.3\text{m}$

Answer 1

The correct option is B $14.7\text{m}$

Here we take the refrence level at the top of the tower. Figure given below shows, the motion scenario of ball.

Initial speed of ball:
$u=+9.8\text{m/s}$
Displacement of ball when it reaches ground:
$S=ut+\frac{1}{2}a{t}^2...\left(i\right)$

Putting $S=-h,a=-9.8{\text{m/s}}^2$ in Equation $\left(i\right)$. We are taking the reference $+ve$ axis as per shown in figure. Hence, $a=-g=-9.8{\text{m/s}}^2$

$\Rightarrow -h=\left(9.8\right)\times t+\frac{1}{2}(-9.8)t^2...\left(ii\right)$
Putting $t=3\text{s}$, we get:
$-h=\left(9.8\right)\times 3+\frac{1}{2}(-9.8)3^2$ $\therefore h=14.7\text{m}$ downward, as measured from top

Hence option B is the correct answer