A diver runs horizontally with a speed of 0.759 m/s off a platform that is 10.0 m above the water. What is his speed just before striking the water
To find the diver's speed just before striking the water, we can use the principle of conservation of energy. The initial potential energy of the diver on the platform is converted into kinetic energy as he falls.
First, let's find the potential energy of the diver when he is on the platform. The potential energy (PE) is calculated using the formula: PE = mgh, where m is the mass of the diver, g is the acceleration due to gravity, and h is the height of the platform.
Given that the height of the platform is 10.0 m and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the formula: PE = m × 9.8 × 10.0.
Next, we need to find the kinetic energy (KE) of the diver just before striking the water. The kinetic energy is given by the formula: KE = 1/2 × m × v^2, where v is the velocity of the diver just before striking the water.
Since energy is conserved, the potential energy when the diver is on the platform is equal to the kinetic energy just before striking the water. Thus, we can set the potential energy equal to the kinetic energy and solve for v.
m × 9.8 × 10.0 = 1/2 × m × v^2
To simplify, we can cancel out the mass (m) on both sides of the equation:
9.8 × 10.0 = 1/2 × v^2
Now, we can solve for v:
v^2 = 2 × 9.8 × 10.0
v^2 = 196
v = √196
v = 14.0 m/s
Therefore, the diver's speed just before striking the water is 14.0 m/s.