Question

From the top of a tower of height 40 m, a ball is projected upwards with a speed of ${20 \,m \, s^{-1}}$ at an angle of elevation of 30?. Then the ratio of the total time taken by the ball to hit the ground to its time to same height is Take ${g = 10 \, m \, s^{-2}}$

• A. 2:01
• B. 3:01
• C. 3:02
• D. 4:01

Answer 1

The Correct Option is A

If $t$ is the total time taken, then
$40 = - 20 \, \sin \, 30^{\circ}\, t + \frac{1}{2} \times 10 \times t^2$
$40 = -20 \sin \, 30^\circ t + 5t^2$
or $40 = - 10 t + 5t^2$
or $5 t^2 - 10t - 40 = 0$
or $t^2 - 2t - 8 = 0$
or $t^2 - 4t + 2t - 8 = 0 $
or $t(t - 4) + 2(t - 4) = 0$
or $(t + 2)(t - 4) = 0$
$ \Rightarrow \, t = 4 \, s$ [Negative time is not allowed]
Time of flight to height of projection
$T= \frac{2u \, \sin \, \theta}{g}$
$ = \frac{2 \times 20 \, \sin \, 30^\circ}{10} s = 2s$
$\therefore \:\:\:\:\: \frac{t}{T} = \frac{4}{2} = \frac{2}{1}$