Refer to Exercises 95 and 96. a. Compute a jumpers terminal velocity, which is defined as b.

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Refer to Exercises 95 and 96.

a. Compute a jumper’s terminal velocity, which is defined as |kg |mg tanh lim v(t) = lim т

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 v(t) = d'(t) = |mg tanh |kg т

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.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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