Question

According to a newspaper account, a paratrooper survived a training jump from 1190 ft when his parachute failed to open but provided some resistance by flapping in the wind. Allegedly he hit the ground at 99 mi/h after falling for 6 seconds. To test the accuracy of this account, you should first find the drag coefficient ?, assuming a terminal velocity of 99 mi/h and also that the resistance of the paratrooper falling through the air is proportional to his velocity.

Remember that the accleration due to gravity near the earth's surface is 32 ft/sec²

Answer 1

To find the drag coefficient in this scenario, we can use the equation for drag force: FD = 0.5 * ? * A * v^2, where FD is the drag force, ? is the drag coefficient, A is the cross-sectional area, and v is the velocity.

Step-by-step explanation:

To find the drag coefficient in this scenario, we can use the equation for drag force: FD = 0.5 * ? * A * v^2, where FD is the drag force, ? is the drag coefficient, A is the cross-sectional area, and v is the velocity. First, we need to convert the terminal velocity of 99 mi/h to ft/s, which is 145.2 ft/s. We can then rearrange the equation to solve for ?:

? = (2 * FD) / (A * v^2)

Substituting the values given in the question, we have:

? = (2 * mg - FD) / (A * v^2)

Where m is the mass of the paratrooper, g is the acceleration due to gravity, and FD is the drag force. We can calculate the value of ? using this equation.