Question

rita throws a ball straight up into the air and catches it at the same position from which she threw it. the ball has 18 j of mechanical energy when it leaves her hand. if no energy is lost due to friction, which statements about the energy of the ball are true? check all that apply. the potential energy at the top of the balls motion is 18 j. the kinetic energy is less when the ball is thrown than when it is caught. the kinetic energy increases as the potential energy decreases. the kinetic energy decreases as the potential energy increases. the total mechanical energy of the ball stays constant. the mechanical energy decreases as the ball moves.

Explanation:

Step1: Understand mechanical - energy conservation

Mechanical energy $E = K+U$. Since no energy is lost to friction, $E$ is conserved.

Step2: Analyze initial and top - position energy

When the ball leaves her hand, $E = 18J$. At the top, $K = 0$ (momentarily at rest), so $U = 18J$.

Step3: Analyze energy conversion

As the ball goes up, $v$ decreases (so $K=\frac{1}{2}mv^{2}$ decreases) and $h$ increases (so $U = mgh$ increases). As it comes down, the opposite occurs. The total mechanical energy $E$ remains 18J throughout the motion.

Answer:

• The potential energy at the top of the ball's motion is 18 J.
• The kinetic energy decreases as the potential energy increases.
• The total mechanical energy of the ball stays constant.