 Hello and welcome to the session, let's work out the following question. It says, a stone dropped from a balloon moving horizontally with a velocity of 40 meter per second reaches the ground in 5 seconds. Find the height of the balloon, the velocity of the stone at the time of striking the ground and its direction. Let's now move on to the solution. We have to find the height of the balloon. So let H be the height of the balloon or let height of the balloon be H meters. Now we are given that the stone is dropped from a balloon moving horizontally. So the velocity of the stone is in the horizontal direction. So the stone is dropped from a balloon moving horizontally with the velocity with the horizontal velocity 40 meter per second. Now since it is moving horizontally, therefore the vertical component of the velocity will be zero. Therefore the vertical component is zero. Now considering the vertical motion of stone we have H is equal to 1 by 2 gt square. As we know that H is given by ut plus 1 by 2 gt square where u is the initial velocity. So H is equal to 1 by 2 g is 10 meter per second square into t which is 5 seconds. This 5 square this is equal to 2 into 5 into 25 which is equal to 125 meter. Thus the height of the balloon is 125 meter. Now let vx and vy be the horizontal vertical components of velocity of the stone on striking the ground. Now we are given that horizontal velocity is 40 meter per second. So we have vx is equal to 40 meter per second and vy square is given by 0 square plus 2 gh. As we know that v is given by v square is equal to u square plus 2 gh where u is the initial velocity and we know that the initial component of the velocity it's a vertical component of the velocity is zero. So the initial velocity is zero in the vertical direction and vy square is given by 0 square plus 2 gh. Let's now substitute the values. We have 0 square plus 2 gh touches 125 meter. So this is equal to this is equal to 2500. So vy is equal to 50. So the vertical component of the velocity is 50 meter per second. Now let v be the resultant velocity of the stone on striking the ground. Therefore v is given by under the root vx square plus vy square which is vx square is 40 square plus 50 square. So this is equal to 40 square is 1600, 2500 which is equal to under the root 4100 which is equal to 10 into under the root 41 meter per second. So this is the velocity of the stone on striking the ground. Now we have to find the direction. So now if the direction of this resultant velocity makes an angle theta with the horizontal and theta is given by vertical component of the velocity upon the horizontal component of the velocity that is vy upon vx. Now vy is 50 and vx is 40. So tan theta is equal to 5 by 4. So this implies theta is equal to tan inverse 5 by 4. Thus the stone strikes the ground with the velocity 10 into under the root 41 meter per second making an angle 5 by 4 with the horizontal or the ground. So this completes the question and the session. Bye for now. Take care. Have a good day.