Speed Calculation of Cliff Divers at Acapulco, Mexico
What is the speed of the cliff divers when they hit the water in Acapulco, Mexico?
1: 1m/s
Answer:
The speed of the cliff divers when they hit the water can be calculated using the formula v = √(2gh), where g is the acceleration due to gravity and h is the height of the cliff.
According to the principle of conservation of energy, the total mechanical energy of a system remains constant if no external forces are acting on it. In this case, we can consider the system to be the diver. At the top of the cliff, the diver possesses potential energy due to their height above the ocean. As they jump off the cliff, this potential energy is converted into kinetic energy, which is the energy of motion. Ignoring air resistance, the total mechanical energy of the system remains constant throughout the dive.
To calculate the speed of the diver when they hit the water, we can equate the initial potential energy to the final kinetic energy. The potential energy at the top of the cliff is given by the formula PE = mgh, where m is the mass of the diver, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the cliff.
The potential energy at the top of the cliff is then converted into kinetic energy at the bottom, which can be calculated using the formula KE = (1/2)mv², where v is the speed of the diver when they hit the water.
Equating the initial potential energy to the final kinetic energy, we have mgh = (1/2)mv². Simplifying this equation, we can cancel out the mass of the diver and solve for v:
gh = (1/2)v² 2gh = v² v = √(2gh)Therefore, the speed of the cliff divers when they hit the water in Acapulco, Mexico can be calculated using the formula v = √(2gh), where g is the acceleration due to gravity and h is the height of the cliff.