Question

select all statements that are true about the cannonball soaring through the air in the picture below. the apex is the highest point of the cannonballs flight. ignore the effects of air resistance. a potential energy remains constant as the cannonball flies through the air. b potential energy is converted to kinetic energy once the cannonball goes past its apex. c the total energy of the cannonball remains constant as it travels through the air. d the kinetic energy of the cannonball decreases until it reaches the apex. e total energy is only constant at the apex.

Explanation:

Step1: Recall energy - conservation principle

In the absence of air - resistance, the total mechanical energy ($E = K+U$) of the cannonball is conserved during its flight.

Step2: Analyze potential and kinetic energy changes

As the cannonball moves upward, its height $h$ increases. The potential energy is given by $U = mgh$, so $U$ increases. Since $E=K + U$ is constant and $U$ increases, the kinetic energy $K=\frac{1}{2}mv^{2}$ decreases. At the apex (highest point), the vertical component of the velocity is 0, and the kinetic energy is at a minimum for the upward - motion part of the trajectory. As the cannonball moves past the apex and falls down, the potential energy decreases and the kinetic energy increases.

Step3: Evaluate each statement

• Statement A: Potential energy changes as the height of the cannonball changes during its flight, so it is not constant. False.
• Statement B: Once past the apex, as the cannonball falls, potential energy is converted to kinetic energy. True.
• Statement C: Total mechanical energy ($E = K + U$) is conserved throughout the flight in the absence of air - resistance. True.
• Statement D: As the cannonball moves upward towards the apex, its speed decreases, so its kinetic energy decreases. True.
• Statement E: Total energy is conserved throughout the flight, not just at the apex. False.

Answer:

B. Potential energy is converted to kinetic energy once the cannonball goes past its apex.
C. The total energy of the cannonball remains constant as it travels through the air.
D. The kinetic energy of the cannonball decreases until it reaches the apex.