A baloon starting from the ground has been ascending vertically at a uniform velocity for 4 sec and a stone - Physics - Motion In A Straight Line

Question

A baloon starting from the ground has been ascending vertically
at a uniform velocity for 4 sec and a stone let fall from it
reaches the ground in 6 sec find te velocity of the balloon and its
height when the stone was let fall (g=10 m/second square)
Please provide step by step solution to problem with the
explanation of the question

Satyendra Singh · Accepted Answer

Consider the following figure to represent the situation:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/Balloon%20JPG"
style="width: 116px; height: 375px;">

Let us consider that the balloon was initially going up at the rate
of u m/s
The balloon after being released from point A will reach point
B(where stone is let fall) after 4s Therefore, Height reached by
the balloon:H = speed*timeH = 4uWhen the balloon is at B, the stone
is let fall At the instant the velocity of the stone is um/s in the
upward direction Or, we can say that its velocity is -u m/s in the
downward direction Therefore, for the motion of stone from B to
A:Initial velocity = -u m/sH=4u mt=6 s (given)from second equation
of motion:h= ut+12gt24u = -u×6+12*10*36or,10 u =
180u=18m/sThe height from which the stone was let fall = 4u H = 72
m