When a body is thrown vertically upwards, it follows a parabolic path due to the influence of gravity. Let's prove that the time of ascent is equal to the time of descent for this motion.
Let's consider the motion of the object from the point of release until it reaches the highest point.
At the start, when the object is thrown upwards, we can consider the initial velocity as u and its acceleration due to gravity as g.
Using the equation of motion for the object in the vertical direction:
v = u + at
At the highest point, the velocity will be zero because the object momentarily stops before changing its direction. Therefore, we can use this condition and the equation of motion to calculate the time taken to reach the highest point. At the highest point,
v = 0, u = initial velocity, a = acceleration due to gravity, t = time taken to reach highest point.
0 = u - gt
u = gt
t = u/g
After reaching the highest point, the object starts falling back. It follows the same parabolic path, so the time taken to reach the highest point is equal to the time taken to fall back to the same point.
So the time of ascent and the time of descent are equal.
Therefore, the time of ascent is indeed equal to the time of descent.
This proves that for an object thrown vertically upwards, the time of ascent is equal to the time of descent.
