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

Category: QuestionsA particle is projected vertically upwards with a velocity of 196 m/sec. What is the value of total time of flight?
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.