## Question

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

### Solution

2 : 1

The time of flight The initial downward velocity = 20 sin 30° = 10 ms^{-1}. The time taken to fall through a height of 40 m with velocity 10 ms^{-1} is given by

or t^{2} + 2*t* – 8 = 0

which gives *t* = 2s. Hence the total time to hit the ground

= *t _{f}* +

*t*= 2 + 2 = 4s

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