From the top of a tower of height 40 m, a ball is projected upwards with a speed of 20 ms-l at an angle of elevation of 30o. Then the ratio of the total time taken by the ball to hit the ground to the time taken to ball come at same level as top of tower.

If t is the total time taken, then    40 = -20 sin 300 t + 12×10×t2or 40 = - 10t+5t2or 5t2- 10t-40 = 0or t2-2t-8 = 0or t2-4t+2t-8 = 0or t(t-4)+2(t-4 ) = 0or (t+2)(t-4) = 0t = 4 s [Negative time is not allowed]T = 2v sin θg = 2×20 sin 30010s = 2 s∴   tT = 42 = 21