Question

A stone is projected from the top of a tower with velocity $20m/s$ making an angle of elevation of ${30}^o$ with the horizontal. If the total time of flight is $5s$ and $g=10m/s^2$, then

• A. the height of the tower is $75m$.
• B. the maximum height of the stone from the ground is $80m$.
• C. both A and B are true.
• D. the height of the tower is $120m$.

Answer 1

Answer: (C)

both A and B are true.

$S_y=ut-\frac{1}{2}g{t}^2$

$h=S_y=20\sin {30}^o\times 5-\frac{1}{2}\times 10\times (5{)}^2$
$h=50-125=-75m$ (minus sign just indicates that the displacement is in downward direction)

$h_{max}=\frac{u^2{\sin }^2\theta }{2g}=\frac{(20{)}^2{\sin }^2{30}^0}{2\times 10}=5m$

Hence, maximum height attained by projectile $=h+h_{max}=75+5=80m$