Question

a diver jumping off a diving board has 2 j of potential energy and 9 j of kinetic energy. as they are falling down to the water, they have 2 j of potential energy and some kinetic energy. how much kinetic energy is present? options: 18 j, 2 j, 11 j, 9 j

Explanation:

Step1: Recall the law of conservation of energy

The total mechanical energy (sum of potential energy \( E_p \) and kinetic energy \( E_k \)) remains constant in the absence of non - conservative forces (like air resistance, which we can assume is negligible here). So, initial total energy \( E_{total, initial}=E_{p, initial}+E_{k, initial} \), and final total energy \( E_{total, final}=E_{p, final}+E_{k, final} \), and \( E_{total, initial} = E_{total, final} \).

Step2: Calculate initial total energy

Initial potential energy \( E_{p, initial} = 2\space J \), initial kinetic energy \( E_{k, initial}=9\space J \). So, \( E_{total, initial}=2 + 9=11\space J \).

Step3: Calculate final kinetic energy

Final potential energy \( E_{p, final} = 2\space J \), and let final kinetic energy be \( E_{k, final} \). Since \( E_{total, initial}=E_{total, final} \), we have \( 11=2 + E_{k, final} \). Solving for \( E_{k, final} \), we get \( E_{k, final}=11 - 2 = 9\space J \)? Wait, no, wait. Wait, initial total energy: \( 2 + 9=11 \). Final potential is 2, so final kinetic is \( 11 - 2=9 \)? Wait, no, maybe I made a mistake. Wait, no, the initial total energy is \( 2+9 = 11 \). When falling, potential energy is still 2, so kinetic energy should be \( 11 - 2=9 \)? But let's check again. Wait, the problem says "as they are falling down to the water, they have 2 J of potential energy". Wait, maybe the initial total energy is \( 2 + 9=11 \), and since mechanical energy is conserved (assuming no energy loss), final total energy is also 11. So final kinetic energy \( E_k=11 - 2 = 9 \)? But the options have 9 J. Wait, but let's re - examine. Wait, the initial state: \( E_p = 2 \), \( E_k=9 \), total \( 11 \). Final state: \( E_p = 2 \), so \( E_k=11 - 2=9 \). So the kinetic energy is 9 J.

Wait, but maybe I messed up. Wait, no, the key is conservation of mechanical energy. The total mechanical energy (potential + kinetic) remains the same. So initial total: \( 2 + 9 = 11 \). Final potential: 2, so final kinetic: \( 11 - 2=9 \). So the answer is 9 J.

Answer:

D. 9 J