Question

A ball is thrown vertically upward attains a maximum height of 45 m. the time after which the velocity of the ball becomes equal to half the velocity of projection is (use g = 10 m/s2)

Answer 1

Given: h=45m  ,  g = 10 m/s2
 
Let the velocity of projection be 'u'. Then 'v' =0  (at top height)

v² =u² -2gh

u= √2gh

u= √2×10×45= √900

u= 30 m/s

velocity becomes half  the velocity of projection 

v= 1/2 ×30= 15 m/s

v = u+ at          (first eq. of motion)

15= 30 - 10t

10t = 30  - 15

10t = 15

t= 15/10 = 1.5 sec

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 The time after which the velocity of the ball becomes equal to half the velocity of projection is = 1.5 sec 
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Hope this will help you.....