A balloon starts from rest, moves vertically upwards with an acceleration g//8ms^(-2). A stone falls from the balloon after 8s from the start. Find the time taken by the stone to reach the ground (g=9.8ms^(-2))

A balloon starts from rest, moves vertically upwards with an accelerat

1.	A balloon starts from rest, moves vertically upwards with an acceleration g//8ms^(-2). A stone falls from the balloon after 8s from the start. Find the time taken by the stone to reach the ground (g=9.8ms^(-2))
Answer» Solution :Step-1 : To FIND the distance of the stone above the ground about which it begins to fall from the balloon. `S=ut+(1)/(2)at^(2)," here, "s=h,u=0,a=g//8` `h=(1)/(2)((g)/(8))8^(2)=4g` Step-2 : The velocity of the balloon at this height can be obtained from `v=u+at` `V=0+((g)/(8))8=g` This becomes the initial velocity `(u^(1))` of the stone as the stone falls from the balloon at the height h. `therefore u^(1)=g` Step-3 : For the total motion of the stone `h=(1)/(2)g t^(2)-u^(1)t` Here, `h=4g,u^(1)=g,t` = time of TRAVEL of stone. `therefore -4g=g t-(1)/(2)g t^(2)` `therefore t^(2)-2t-8=0` solving for .t. we GET `t=4 and -2s`. Ignoring negative value of time, `t=4s`.