Question

A ball thrown vertically upwards with a speed of $19.6{\text{ms}}^{-1}$ from the top of a tower returns to the earth in $6\text{s}$. Find the height of the tower.
(Take $g=9.8{\text{m/s}}^2$)

• A. $27.8\text{m}$
• B. $58.8\text{m}$
• C. $70\text{m}$
• D. $92\text{m}$

Answer 1

The correct option is B $58.8\text{m}$


Sign convention: Taking upward positive.
Given that,
Initial velocity of ball, $u=19.6{\text{ms}}^{-1}$
Acceleration due to gravity, $g=-9.8{\text{ms}}^{-2}$
Time taken by ball to return ground, $t=6\text{s}$
Let the height of the building is $h$
Net displacement, $s=-h$
By using the $2$nd equation of motion
$s=ut+\frac{1}{2}g{t}^2$
Substitute values
$\Rightarrow -h=19.6\times 6+\frac{1}{2}\times (-9.8)\times 6^2$
$\Rightarrow -h=117.6-176.4$
$\Rightarrow -h=-58.8$
$\Rightarrow h=58.8m$
Hence, option (b) is correct.