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? 9 j 11 j 2 j 18 j

Explanation:

Step1: Recall conservation of mechanical energy

The total mechanical energy (sum of potential and kinetic energy) should remain constant (assuming no non - conservative forces like air resistance are significant here). So, initial total energy \(E_{total, initial}=E_{p, initial}+E_{k, initial}\).
Initial potential energy \(E_{p, initial} = 2\space J\), initial kinetic energy \(E_{k, initial}=9\space J\), so \(E_{total, initial}=2 + 9=11\space J\).

Step2: Calculate final kinetic energy

Final potential energy \(E_{p, final} = 2\space J\), and total energy \(E_{total, final}=E_{total, initial}=11\space J\) (due to conservation of mechanical energy). We know that \(E_{total, final}=E_{p, final}+E_{k, final}\). So, \(E_{k, final}=E_{total, final}-E_{p, final}\).
Substituting the values, \(E_{k, final}=11 - 2 = 9\space J\)? Wait, no, wait. Wait, initial total energy is \(2 + 9=11\space J\). Final potential energy is \(2\space J\), so final kinetic energy is \(11-2 = 9\space J\)? But wait, that seems conflicting? Wait, no, maybe I made a mistake. Wait, when the diver is jumping off, initial potential energy (relative to the water) and initial kinetic energy. As they fall, potential energy changes, but total mechanical energy (PE + KE) should be conserved. Wait, initial PE is 2J, initial KE is 9J, so total is 11J. Final PE is 2J, so final KE is 11 - 2=9J? But that would mean KE doesn't change? Wait, maybe the initial PE is different? Wait, no, the diagram shows initial \(E_p = 2J\), \(E_k=9J\), and when falling, \(E_p = 2J\). Wait, that would imply that the height doesn't change, which doesn't make sense. Wait, maybe the problem has a typo, or maybe I misinterpret the PE. Wait, perhaps the initial PE is, say, when on the board, and when falling, the PE is still 2J (maybe the reference point is such that at the water level, PE is 0, but maybe the diver is not at the water level yet). Wait, no, according to the problem, we have to go with the numbers given. So initial total energy: \(E_{total}=E_p + E_k=2 + 9 = 11\space J\). Final \(E_p = 2\space J\), so \(E_k=E_{total}-E_p=11 - 2 = 9\space J\)? But that would mean that the kinetic energy is 9J. But let's check the options. The options are 9J, 11J, 2J, 18J. So 9J is an option. Wait, but maybe my understanding of conservation is wrong. Wait, another way: maybe the initial total energy is \(E_p+E_k\), and when falling, the PE is converted to KE, but if PE remains the same, then KE should remain the same. So if initial KE is 9J and PE is 2J, and final PE is 2J, then KE is 9J. So the answer should be 9J.

Wait, no, wait, maybe the initial PE is, for example, when the diver is at the diving board, and when they are falling, the PE is still 2J (maybe the diving board and the point where we measure the final PE are at the same height). So in that case, since PE doesn't change, KE also doesn't change. So KE remains 9J.

Answer:

9 J (the option with 9 J)