Question

An object is thrown horizontally from a point '$A$' from a tower and hits the ground $3s$ later at $B$. The line from '$A$' to '$B$' makes an angle of ${30}^{\circ }$ with the horizontal. The intial velocity of the object is :
(take g = 10 $m/s^2$)

• A. $15\sqrt{3}m/s$
• B. $15m/s$
• C. $10\sqrt{3}m/s$
• D. $\frac{25}{\sqrt{3}}m/s$

Answer 1

The correct option is A $15\sqrt{3}m/s$

Object takes $3s$ to fall.
Hence AC = height $=\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times 9=45m$
Also:
$tan{30}^{\circ }=\frac{AC}{BC}=\frac{1}{\sqrt{3}}$
$BC=\sqrt{3}AC=45\sqrt{3}m$
The object covers AB in $3s$, hence initial velocity $=\frac{BC}{3}=15\sqrt{3}m{s}^{-1}$