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

(a) 40 sec

(b) 45 sec

(c) 50 sec

(d) 55 sec

I had been asked this question by my college professor while I was bunking the class.

Origin of the question is Calculus Application topic in division Application of Calculus of Mathematics – Class 12

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The correct option is (a) 40 sec

For explanation: 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 [where, v = dx/dt] ……….(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)gt^2 ……….(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)gT^2

Or gT = 2u

Or T = 2u/g = 2(196)/9.8 [as, g = 9.8m/sec^2]

= 40 sec.