A student of mass m is at a swimming pool. She climbs the steps to the diving board 4.0 m above the water. She jumps off the board, which enables her to rise a further 0.7 m before she begins her descent into the pool. At what speed does she enter the water?

You may assume that the acceleration due to gravity, g, is 9.8 m s−2.

Your answer for this question should be presented under these three headings:

Decide how you are going to
tackle the problem.
Do the calculation.
Check that your answer makes sense.

mg(H+h)=mv²/2

v = sqrt{2g(H+h)}

stop cheating and do your test

Decide how you are going to tackle the problem:

To determine the speed at which the student enters the water, we can use the principle of conservation of mechanical energy. The mechanical energy at the top of the diving board (when the student is at rest) is equal to the mechanical energy at the highest point of her jump before she begins her descent. We can consider the mechanical energy at the highest point as the sum of the potential energy and the total kinetic energy.

Do the calculation:
We can start by calculating the potential energy at the top of the diving board using the formula:

Potential energy = mass * gravitational acceleration * height

Given that the mass (m) is provided, and the gravitational acceleration (g) is 9.8 m/s², and the height (h) is 4.0 m, the potential energy at the top is:

Potential energy = m * g * h

Next, we need to calculate the total mechanical energy at the highest point of the jump. Since the student is at rest, the initial kinetic energy is zero. Therefore, the total mechanical energy is equal to the potential energy:

Total mechanical energy = Potential energy

Now we can calculate the kinetic energy at the highest point before the student begins her descent using the formula:

Kinetic energy = 0.5 * mass * velocity^2

Since the initial kinetic energy is zero, the kinetic energy is equal to the total mechanical energy at the highest point:

Total mechanical energy = Kinetic energy

Finally, we can solve for the velocity (v) using the formula:

velocity = sqrt(2 * Total mechanical energy / mass)

Substituting the known values, we can calculate the velocity.

Check that your answer makes sense:
We can verify the obtained answer by considering the physical context of the problem. The speed at which the student enters the water should be a realistic value and within a reasonable range for such a jump.