JEE Class main Answered

Equation of motion that relates velocity as a function of time for the stone projected vertically is

v = u - g t ................................ (1)

where v is velocity at time t , u is initial  projection velocity and g is acceleration due to gravity.

when the stone reaches maximum height , we have v = 0 .

If time of flight is 8 s , then time to reach maximum height is 4 s

Hence from eqn.(1) , we get initial projection velocity u as

u = g t = 10 × 4 m/s = 40 m/s

------------------

Equation of motion that gives displacement as a function of time is

S = u t - (1/2) g t²

Hence displacement at time t = 6 s is

S = ( 40 × 6 ) - ( 0.5 × 10 × 6 × 6 )  m = 60 m