A 65 kg woman dives from a 10 m platform. What is her speed as she enters the water.
To find the speed of the woman as she enters the water, we can use the principle of conservation of energy. The potential energy she possesses at the top of the platform will be converted into kinetic energy as she falls.
First, let's calculate the potential energy (PE) at the top of the platform. The potential energy can be calculated using the formula:
PE = m * g * h
Where:
m = mass of the woman = 65 kg
g = acceleration due to gravity = 9.8 m/s²
h = height of the platform = 10 m
PE = 65 kg * 9.8 m/s² * 10 m
PE = 6370 N·m (or Joules)
Next, let's calculate the kinetic energy (KE) at the moment she enters the water. The kinetic energy can be calculated using the formula:
KE = 0.5 * m * v^2
Where:
m = mass of the woman = 65 kg
v = speed of the woman
Since the potential energy is converted into kinetic energy, we can equate them:
PE = KE
6370 N·m = 0.5 * 65 kg * v^2
Simplifying the equation:
6370 N·m = 32.5 kg * v^2
Dividing both sides by 32.5 kg:
v^2 = 195.7 m²/s²
Taking the square root of both sides:
v ≈ 14 m/s
Therefore, the speed of the woman as she enters the water is approximately 14 m/s.