Question

A body is thrown vertically upward such that the distance travelled by it in fifth and sixth second are equal .the maximum height reached by body is

Answer 1

If the ball covers equal distances in the 5th second and 6th second, it would only be possible if the ball reaches the maximum height at the end of the 5th second (or the beginning of the 6th second).
This is because, when a ball is following vertical motion, it is always under the action of gravity. Therefore, it will have a constant acceleration acting on it all the time.
However, when the ball is thrown up, is velocity is against the direction of gravity and the distance it covers in each consecutive second is always less than the distance covered in the previous second and it continues moving up till its velocity becomes zero. This point is when the ball has achieved the maximum height.
On the other hand, of the ball is released from a height, its direction of velocity is along the direction of propagation of gravity. Hence, the distance it covers in one second is always lesser than the distance it will cover in the succeeding second.
Applying equations of motion,
FIRST EQUATION:
v = u - gt
At highest point, v = 0
therefore 0 = u - (9.8)(5) implies u = 49 m/s
SECOND EQUATION:
s = ut + {1}/{2} g{t}^2
s = 49(5) - 4.9(25)= 245 - 122.5 = 122.5m