A particle is projected vertically upwards with a velocity of 196 m/sec. What is the value of total time of flight?

A particle is projected vertically upwards with a velocity of 196 m/sec. What is the value of total time of flight? Correct Answer 40 sec

Let the particle projected from A with velocity u = 196 m/sec and P be its position at time t where, AP = x m, if v m/sec be its velocity at P,then the equation of motion of the particle is, dv/dt = -g ……….(1) Since v = u, when t = 0, hence from (1) we get, u∫vdv = -g 0∫tdt Or v – u = -gt Or dx/dt = u – gt ……….(2) Since x = 0, when t = 0, hence from (2) we get, 0∫x dx = 0∫x (u – gt)dt Or x = ut – (1/2)gt2 ……….(3) If T(≠0) be the total time of flight, then x = 0, when t = T; hence, from (3) we get, Or 0 = uT – (1/2)gT2 Or gT = 2u Or T = 2u/g = 2(196)/9.8   = 40 sec.