Understanding the Physics
* Constant Acceleration: In a vacuum, the only force acting on the body is gravity. This means the acceleration due to gravity (g) is constant throughout the motion.
* Symmetry: The upward and downward paths of the body are symmetrical. This means the speed at which the body is launched upwards is the same as the speed it has when it returns to the launch point.
Derivation
1. Upward Motion:
* Initial velocity = u
* Final velocity at the highest point = 0 (the body momentarily stops)
* Acceleration = -g (negative because it opposes the upward motion)
Using the equation of motion: v = u + at
We get: 0 = u - gt1 (where t1 is the time taken to go up)
Therefore, t1 = u/g
2. Downward Motion:
* Initial velocity = 0 (starts from rest at the highest point)
* Final velocity = u (same as the initial velocity upwards)
* Acceleration = g (positive because it acts in the direction of motion)
Again using v = u + at, we get: u = 0 + gt2 (where t2 is the time taken to come down)
Therefore, t2 = u/g
Conclusion
As you can see, both t1 and t2 are equal to u/g. Therefore, the time taken to go up and come down is the same.
Key Point: This analysis holds true only in a vacuum. In the real world, air resistance will cause the time taken to come down to be slightly longer than the time taken to go up.
