You are on the top of a high building. You have 3 identical balls which you throw with same initial velocity; one vertically upwards, one vertically downwards and one horizontally straight.Which ball will have the maximum velocity on reaching the ground? (Ignore air resistance)
Answers
A student at the top of building of height h throws one ball upward with the initial speed V and then throws a second ball downward with the same initial speed. How do the final speeds of the balls compare when they reach the ground?
The two balls will reach the ground with same velocity but after a time delay as one is thrown up and another one down from a place whose height say h .
As the acceleration due to gravity say g m/s^2 is acting uniformly during the whole journey of the two balls….
The first one which was thrown above will slowly loose its kinetic energy in working against g initially and coming to a height say h1 above the point of projection when its final velocity is zero
(1/2) m. v^2 = m . g . h1
,will return back to the same height h and with the same velocity as the velocity of projection but directed downward…(energy conservation holds)
so this ball reaches the same energy state as the second ball which was projected downwards with the same velocity v.
so, the two covering height h with g acting downwards will come to same final velocity say Vf
Vf^2 - v^2 = 2. g. h
Vf = Sqrt { v^2 + 2.g. h } for both the balls