A particle is projected with velocity 2 g h so that it just clears two walls of equal height h , which are at a distance of 2 h from each other. What is the time interval of passing between the two walls?

Step-by-step solution

Let t be the time interval. Then, 2 h = u x ( t ) or u x = 2 h t ...(i) Further, h = u y t - 1 2 g t 2 or g t 2 - 2 u y t + 2 h = 0   t 1 = 2 u y + 4 u y 2 - 8 g h 2 g and t 2 = 2 u y - 4 u y 2 - 8 g h 2 g t = t 1 - t 2 = 4 u y 2 - 8 g h g or u y 2 = g 2 t 2 4 + 2 g h ...(ii) Given, u x 2 + u y 2 = 2 g h 2   4 h 2 t 2 + g 2 t 2 4 + 2 g h = 4 g h g 2 4 t 4 - 2 g h t 2 + 4 h 2 = 0 t 2 = 2 g h ± 4 g 2 h 2 - 4 g 2 h 2 g 2 / 2 = 4 h g or t = 2 h g