# Three identical balls are thrown from a cliff of height, h, above a horizontal plane. One ball is...

## Question:

Three identical balls are thrown from a cliff of height, h, above a horizontal plane. One ball is thrown at an angle of 45 degrees above the horizon, the second is thrown horizontally, and the third is thrown at an angle of 30 degrees below the horizon (so, part of this velocity is downward). If all the balls are given the same initial speed, which one will have the greatest speed at the moment just before it hits the ground?

## Projectile motion:

If an object is thrown from the edge of the cliff, then it travels under acceleration due to gravity. The object traces a parabolic path to the ground level.

Due to this acceleration the vertical velocity of the object increases.

The horizontal component of the velocity remains constant.

The height of the cliff is, h.

One ball is thrown at an angle of 45 degrees.

The second is thrown horizontally

The third ball is thrown at an angle of 30 degrees below the horizontal

The initial speeds of each ball are the same.

Here, we use energy conservation.

Each ball is initially at the same height and has the same speed. So, each ball has the same mechanical energy at the initial height point.

All the balls fall to the ground level.

So their final kinetic energies are also equal.

Balls are identical, so their velocities will also be equal at the ground level.

Thus all three balls will have equal speeds at the ground. 