To determine the child's speed just before hitting the water, we can use the principle of conservation of energy, assuming there is no air resistance.
The potential energy (PE) of the child at the top of the dive platform is given by:
PE = m * g * h
Where:
m = mass of the child (40 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the dive platform (10 m)
Substituting the given values, we get:
PE = 40 kg * 9.8 m/s^2 * 10 m = 3920 J
This potential energy is converted entirely into kinetic energy (KE) just before hitting the water. The kinetic energy is given by:
KE = 1/2 * m * v^2
Where:
v = velocity of the child just before hitting the water
We can rearrange the equation to solve for v:
v = √(2 * KE / m)
Substituting the potential energy (PE) for kinetic energy (KE), we get:
v = √(2 * PE / m)
v = √(2 * 3920 J / 40 kg) ≈ √(196) ≈ 14 m/s
So, the child is moving at approximately 14 meters per second just before hitting the water.
