Astudent 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?

They are the same (assuming there is no air friction)

Explanation:

Take a look at the picture.

When the first ball (the one thrown upward) gets to the point marked as A, the speed will has the exact same value V but the velocity will now point downward (just like the second ball).

So if you think about it, the first ball, from point A to the ground, will behave exactly like the second ball (same initial speed, same height).

That is why the speeds will be the same when they reach the ground.

Velocity is same

Explanation:

Case I:

When the ball throws upwards

Let the velocity of the ball as it hits the ground is V'.

Initial velocity, u = V

Final velocity, v = V'

height = h

acceleration due to gravity = g

Use third equation of motion

By substituting the values

     .... (1)

Case II:

When the ball throws downwards

Let the velocity of the ball as it hits the ground is V''.

Initial velocity, u = V

Final velocity, v = V''

height = h

acceleration due to gravity = g

Use third equation of motion

By substituting the values

     .... (2)

By comparing the equation (1) and equation (2), we get

V' = V''

Thus, the velocity of balls in both the cases is same as they strikes the ground.

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