Calculating Maximum Height and Vertical Speed of a Diver

Questions:

a) What is the maximum height in meters that the diver’s center of mass reaches after coming off the diving board during the dive?

b) What is the diver’s vertical speed in m/s when their hands first hit the water during the dive?

Answers:

Final answer: The maximum height reached by the diver's center of mass after coming off the diving board during the dive is approximately 4.54 meters. The diver's vertical speed when their hands first hit the water during the dive is approximately 6.15 m/s.

Explanation:

Maximum Height Calculation: To calculate the maximum height reached by the diver's center of mass, we can use the principle of conservation of mechanical energy. The potential energy gained by the diver is equal to the potential energy lost by the springboard.

First, let's calculate the potential energy lost by the springboard using the formula: PE_springboard = (1/2) * k * x^2 where k is the stiffness of the springboard (9000 N/m) and x is the compression of the springboard (0.36 meters). Substituting the values, the potential energy lost by the springboard is 583.2 J.

Next, calculate the potential energy gained by the diver using the formula: PE_diver = m * g * h where m is the mass of the diver (56 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the maximum height reached. Solving the equation, the maximum height reached by the diver's center of mass is approximately 4.54 meters.

Vertical Speed Calculation: To calculate the diver's vertical speed when their hands first hit the water, we use the principle of conservation of mechanical energy.

Assume the initial potential energy of the diver is equal to the potential energy gained when their hands hit the water. Using the formula for potential energy and kinetic energy, the vertical speed of the diver when their hands first hit the water is approximately 6.15 m/s.