Two stones are projected simultaneously with same speed from a point, H m above the ground. One stone thrown vertically upwards, reaches the ground in 8 seconds, while the other stone thrown vertically downwards, touches the ground in 6 seconds. The value of H is

according to question: both stones are projected with same speed let the speed of projection be U. let the stone that is throwwn vertically upards be = A and the stone that is thrown vertically dowwnwards be = B SIGN CONVENTIONS: intitial velocity of stone A= U initial velocity of stone B= -U displacement of stone A and stone B = -H acceleration due to gravity= -g =-10m/s^2 time taken by stone A= 8 sec time taken by stone B = 6 sec FOR STONE A: using s=ut + at^2/2 -H=U * 8+(-10) *8 *8/2 -H=8U-320..................EQUATION 1 FOR STONE B: -H= -U *6+(-10) *6*6/2 -H = -6U-180 U=H/6-180/6..................EQUATION 2 putting value of U obtained from equation 2 into equattion 1 we get; -H=8(H/6-180/6)-320 -3H=4H- 720-960 1680=7H H=240 m