Refer to Exercises 95 and 96.

a. Compute a jumper’s terminal velocity, which is defined as

b. Find the terminal velocity for the jumper in Exercise 96 (m = 75 kg and k = 0.2).

c. How long does it take any falling object to reach a speed equal to 95% of its terminal velocity? Leave your answer in terms of k, g, and m.

d. How tall must a cliff be so that the BASE jumper (m = 75 kg and k = 0.2) reaches 95% of terminal velocity? Assume that the jumper needs at least 300 m at the end of free fall to deploy the chute and land safely.

Data from Exercise 96

Refer to Exercise 95, which gives the position function for a falling body. Use m = 75 kg and k = 0.2. 

Confirm that the base jumper’s velocity t seconds after jumping is

Data from Exercise 95

When an object falling from rest encounters air resistance proportional to the square of its velocity, the distance it falls (in meters) after t seconds is given bywhere m is the mass of the object in kilograms, g = 9.8 m/s² is the acceleration due to gravity, and k is a physical constant.

Transcribed Image Text:

|kg |mg tanh lim v(t) = lim т v(t) = d'(t) = |mg tanh |kg т