Abaseball is thrown vertically upward and feels no air resistance. as it is rising:
a) its kinetic energy is conserved, but its momentum is not conserved.
b) both its momentum and its kinetic energy are conserved.
c) its momentum is not conserved, but its mechanical energy is conserved.
d) both its momentum and its mechanical energy are conserved.
e) its gravitational potential energy is not conserved, buts its momentum is conserved.

C) Its momentum is not conserved, but its mechanical energy is conserved.

Explanation:

There is no air resistance acting on the ball: this means that there are only conservative forces acting on the ball, therefore the total mechanical energy of the ball is conserved.

The total mechanical energy is defined as

where

U is the gravitational potential energy

K is the kinetic energy

The gravitational potential energy is given by:

where m is the mass, g the acceleration of gravity, h the heigth - since the height change, U changes as well, so the potential energy is not conserved.

The kinetic energy is given by

where v is the speed of the ball: as the ball rises, its speed decreases, so the kinetic energy is not conserved as well.

The momentum of the ball is given by:

As we stated above, the speed of the ball is decreasing, so v is decreasing, and this means that the momentum is also not conserved.

So the only correct choice is

C) Its momentum is not conserved, but its mechanical energy is conserved.

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