Question

From the top of the tower of height $40m$, a ball is projected upwards with a speed of $20m/s$ at an the angle of elevation of ${30}^{\circ }$, The ratio of the total time taken by the ball to hit the ground to fits time of flight (time is taken to come back to the same elevation) is (take $g=10m/s^2)$

• A. $2:1$
• B. $3:1$
• C. $3:2$
• D. $1.5:1$

Answer 1

Answer: (A)

$2:1$

We have the equation,

$S=ut+\frac{1}{2}a{t}^2$

That is,

$40=-20sin30t+\frac{1}{2}\times 10\times t^2$

$40=-10t+5t^2$

$5t^2-10t-40=0$

$t^2-4t-8=0$

$t^2-4t+2t-8=0$

$t(t-4)+2(t-4)=0$

$(t+2)(t-4)=0$

That is, $t=4$

Also,

$T=\frac{2vsin\theta }{g}=\frac{2\times 20sin30}{10}=2s$

Therefore,

$\frac{t}{T}=\frac{4}{2}=\frac{2}{1}$

So the ratio is $2:1$