Question

A ball is thrown vertically downward with a velocity of $20\text{m/s}$ from the top of a tower. It hits the ground after some time with a velocity of $80\text{m/s}$. The height of the tower is :
$(g=10{\text{m/s}}^2)$

• A. $320\text{m}$
• B. $300\text{m}$
• C. $360\text{m}$
• D. $340\text{m}$

Answer 1

The correct option is B $300\text{m}$


Let the height of the tower is $h$.

The motion of the ball is constant accelerating motion with acceleration $g=10m/s^2$.

Initial velocity of ball, $u=20\text{m/s}$
Final velocity of ball, $v=80\text{m/s}$

According to equation of motion for constant accelerating motion,
(Here, downward direction is negative and upward direction is positive)

$$v^2-u^2=2(-g)(-h)$$

$\Rightarrow v^2-u^2=2gh$

$\Rightarrow (80{)}^2-(20{)}^2=2\left(10\right)h$

$\Rightarrow 6400-400=20h$

$\Rightarrow 6000=20h$

$\Rightarrow h=300\text{m}$