 Hi and welcome to the session. Let's work out the following question. The question says, a stone is projected vertically upward with a velocity sufficient to carry it to a height of 50 meter. Find its velocity of projection and the time taken to come back to the ground. Use g equal to 9.8 meter per second square. So let's start with the solution to this question. First of all, let u be the velocity of the stone projected vertically upward. Then, v is equal to 0, s is equal to 50 meter that is the distance and g will be minus 9.8 meter per second square. Now, applying the equation of motion v square minus u square equal to 2 a s, we get 0 minus u square is equal to 2 into minus 9.8 into 50. This is equal to minus 980. So this implies that u square is equal to 980 and this implies that u is equal to square root of 980 meter per second. That is equal to 14 square root 5 meter per second. Now, let t be the time taken to reach the highest point then s is equal to ut minus half gt square implies that 50 is equal to square root of 980 into t minus 9.8 by 2 t square. This implies 4.9 t square minus 14 root 5 t plus 50 is equal to 0. t will be equal to minus b plus minus square root b square minus 4 ac divided by 2 a where this is a, this is b along with the negative sign and this is c. So, we will simply put in the values and we have 14 root 5 plus minus square root of 980 minus 4 into 4.9 into 50 divided by 2 into 4.9. This is equal to 14 root 5 divided by 2 into 4.9 because this is equal to 980 and this becomes 0. But the time taken by the stone going upward and downward is the same therefore total time taken by the stone to come back to the ground is equal to 2 into t seconds. That is equal to 2 into 14 root 5 divided by 2 into 4.9. 2 gets cancelled with 2 here we have 10 in the numerator when we have and this is equal to 20 root 5 divided by 7 seconds which is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.