A 65.0 kg professional diver performs a dive from a platform 10 m above the water surface. Find the average impact force she experiences in her collision with the water if the collision lasts for 0.800 s.
To find the average impact force experienced by the diver, we can use the equation:
Force = (mass × acceleration)
First, let's find the acceleration experienced by the diver during the collision. We can use the equation of motion:
Displacement = initial velocity × time + (1/2) × acceleration × time^2
Since the diver falls vertically downwards, the displacement is equal to the height of the platform, which is 10 m. The initial velocity is 0 m/s (because the diver is stationary at the beginning). Let's substitute these values into the equation:
10 m = 0 m/s × (0.8 s) + (1/2) × acceleration × (0.8 s)^2
Simplifying the equation gives:
10 m = (1/2) × acceleration × (0.64 s^2)
Now, let's solve for the acceleration:
acceleration = 10 m / ((1/2) × (0.64 s^2))
acceleration = 10 m / (0.32 s^2)
acceleration = 31.25 m/s^2
Now that we have the acceleration, we can calculate the force experienced by the diver:
Force = mass × acceleration
Force = 65.0 kg × 31.25 m/s^2
Force = 2031.25 N
Therefore, the average impact force experienced by the diver is 2031.25 N.