Question

A body is thrown with a velocity of $20m{s}^{-1}$ from a building of height $15m$. If the angle of projection is ${30}^{\circ }$ above the horizontal, the time of flight and the range of the projectile are respectively.
(Take $g=10m/s^2$)

• A. $1s,30m$
• B. $3s,30m$
• C. $3s,30\sqrt{3}m$
• D. $1s,30\sqrt{3}m$

Answer 1

The correct option is C $3s,30\sqrt{3}m$

Displacement of the body in the vertical direction when the body reaches the ground $=-15m$
(Take downward direction as –ve)
Using second equation of motion, we get
$-H=u\sin \theta \times t-\frac{1}{2}g{t}^2$
$\Rightarrow -15=20\times \frac{1}{2}\times t-5t^2$
$\Rightarrow 5t^2-10t-15=0$
$\Rightarrow t^2-2t-3=0$
$\Rightarrow t=3s$ (Neglecting negative value)
Range of the projectile $=u\cos \theta \times t$
$=20\times \frac{\sqrt{3}}{2}\times 3$
$=30\sqrt{3}m$