Question

A boy playing on the roof of a $10m$ high building throws a ball with a speed of $10m/s$ at an angle of ${30}^{\circ }$ with the horizontal. The time taken by the ball to cross the point which is at the height of $10m$ from the ground is

• A. $1s$
• B. $2s$
• C. $3s$
• D. $4s$

Answer 1

The correct option is A $1s$

Since, the height of the building and the point is same, the ball will touch the point at a distance $R$ from the point of projection, where $R$ is the Range of projectile.

$\therefore$ $R=\frac{u^2\sin 2\theta }{g}=\frac{\left(10{)}^2\sin \right(2\times {30}^{\circ })}{10}$
$⟹R=5\sqrt{3}$
Hence, time taken by the ball to cross the point is
$t=\frac{R}{u\cos \theta }=\frac{5\sqrt{3}}{10\cos \left({30}^{\circ }\right)}$
$⟹t=1s$