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A ground to ground projectile projected at t=0 is at point A at t=T/3 is at point B at t=5T/6 and reaches the ground at t=T. The difference in heights between point A and B is

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Let heights difference between A and B = H

Given :-

t = T/3

t = 5T/6

As we know that, Time of Flight,

T = 2u Sinθ/g

u Sinθ = gT/2 ------(1)

For A,

h = usinθ t - 1/2 gt²

h = usinθ × T/3 - gT²/18

h = gT²/6 - gT²/18

h = 2gT²/18

For B,

h' = usinθ t - 1/gt²

h' = gT/2 × 5T/6 - 1/2 g 25T²/36

h' = 5gT²/12 - 25gT²/72

h' = 5gT²/72

Again,

H = h - h' = 2gT²/18 - 5gT²/72

H = (8gT² - 5gT²)/72

H = 3gT²/72

= gT²/24

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