Question

A ball thrown vertically upwards with a speed of $20m/s$ from the top of a tower reaches a certain height and then falls back to the earth in $6s.$ Find the height of the tower. [Take acceleration due to gravity, $g=10m/s^2$]

• A. $150m$
• B. None of these
• C. $160m$
• D. $100m$

Answer 1

The correct option is C

$160m$

Let the height reached by the ball when thrown upwards be $H$ and the height of the tower be $h$.

Here,

Initial velocity, $u=20m/s$

Final velocity after reaching height, $H$ is $v=0$

acceleration, $a=-g=-10m/s^2$ [It is taken as negative because the direction of acceleration due to gravity is downwards, while the initial velocity is upwards]

Using, $v^2=u^2+2as$

$0={20}^2-2gH$

$H=\frac{{20}^2}{2g}=\frac{20\times 20}{20}=20m$

Now, the ball will fall down from a height of $20m$ from above the tower.

Initial velocity, $u^{\prime }=0$

time, $t=6s$

displacement, $s=20+h$

acceleration, $a=g=10m/s^2$

Using $s=ut+\frac{1}{2}a{t}^2$,

$20+h=0\times 6+\frac{1}{2}\times 10\times 6\times 6$

$\Rightarrow 20+h=180$

$\Rightarrow h=180-20=160m$

Thus, the height of the tower is $160m$