. A parachutist jumps from a plane at 8000 ft altitude with a 24-ft diameter chute.
Total weight of the jumper and the chute is 185 lbs. Determine the time to fall from
8000 ft to 5000 ft using the average fall velocity between the two elevations.
To determine the time it takes for the parachutist to fall from 8000 ft to 5000 ft using the average fall velocity between the two elevations, we need to calculate the fall velocity at each elevation.
To get started, we can use the equation for gravitational potential energy to determine the potential energy at each altitude:
Potential Energy = mass * gravity * height
Since the total weight of the jumper and the chute is given as 185 lbs, we need to convert it to mass in order to use it in the equation. We can do this by dividing the weight in pounds by the acceleration due to gravity, which is approximately 32.2 ft/s^2:
Mass = 185 lbs / 32.2 ft/s^2
Next, we can calculate the potential energy at each altitude:
Potential Energy at 8000 ft = Mass * gravity * 8000 ft
Potential Energy at 5000 ft = Mass * gravity * 5000 ft
Now, the change in potential energy between the two elevations is given by:
Change in Potential Energy = Potential Energy at 8000 ft - Potential Energy at 5000 ft
We can use the equation for potential energy and divide the change in potential energy by the mass to get the change in height:
Change in Height = Change in Potential Energy / Mass
The average fall velocity between the two elevations is then equal to the change in height divided by the time it takes to fall that distance.
Average Fall Velocity = Change in Height / Time
Rearranging the equation, we can solve for time:
Time = Change in Height / Average Fall Velocity
Using this formula, we can calculate the time it takes for the parachutist to fall from 8000 ft to 5000 ft using the average fall velocity between the two elevations.