Question

If an average-sized man jumps from an airplane with an open parachute, his downward velocity t seconds into the fall is V(t) = 20 ( 1-0.2t ) feet per second. Explain how the velocity increases with time.Include in your explanation a comparison of more than one calculated average rate of change (ARC). Find the terminal velocity. Find the time it takes to reach 99% of terminal velocity. Compare your answer in part C with the time it took to reach 99% of terminal velocity on the 2.1 Additional Worksheet part d for a free falling skydiver. On the basis of that information, which would you expect to reach 99% of terminal velocity first, a feather or a cannonball? Explain your reasoning.

Answer 1

A

The rate of change of velocity(deceleration) is constant. So the velocity decreases constantly based on the given function.

Therefore, the deceleration is

Some ARC's:

For, all intervals the rate of change is negative and same. i.e.-the velocity decreases and the rate of decrement is constant in time.

B

The terminal velocity:

(I'l be using SI units for calculation)

is the mass of the object (in this case the man).

density of the fluid (air in this case).

drag coefficient due to a parachute.

area of the parachute (about 400 sq ft)

We will ignore the mass of the parachute.

Plugging in the values,

C

99% of the terminal velocity:

Using the formula,

D

The area is now drastically reduced since there is no parachute.

The area is now about 1 sq ft (0.092 m^2)

and the drag coefficient as about 1.1

So the terminal velocity:

Based on the given function, to reach velocities close to this value, time will be negative. Maybe the function is incorrect. Anyway. if the function is indeed linearly decreasing, this terminal velocity will be reached lot quicker than the one with a chute.

Based on the terminal velocity formula, it is clear that there is an explicit mass dependence.

Thus the feather will have a very small terminal velocity compared to the cannonball. Therefore, the cannonball will reach 99% of its terminal velocity first based on the given function.