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/s2)

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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/s2)

Solution

Correct option is

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              t2 + 2t – 8 = 0

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

                       = tf + t = 2 + 2 = 4s

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