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 need to apply the principle of conservation of energy.
The initial energy of the diver consists of two parts: kinetic energy (due to horizontal motion) and potential energy (due to being at a height above the water). Just before he strikes the water, all of his initial potential energy is converted into kinetic energy. Therefore, we can equate the two energies:
Kinetic Energy = Potential Energy
The kinetic energy can be calculated using the formula:
Kinetic Energy = (1/2) * mass * speed^2
Since the diver's mass is not provided, we can eliminate it from the equation by using the assumption that mass cancels out in the calculation.
Therefore, we have:
(1/2) * speed_initial^2 = mass * g * height
Where:
- speed_initial is the initial speed of the diver (0.759 m/s)
- g is the acceleration due to gravity (9.8 m/s^2)
- height is the height of the platform above the water (10.0 m)
Rearranging the equation, we can solve for the final speed:
speed_final = sqrt(2 * g * height + speed_initial^2)
Now, we can substitute the given values into the equation:
speed_final = sqrt(2 * 9.8 m/s^2 * 10.0 m + 0.759 m/s)^2
Calculating this expression gives us the answer:
speed_final ≈ 14.5 m/s
Therefore, the diver's speed just before striking the water is approximately 14.5 m/s.