Query 09 Differential Equations

Question:  3.6.4.  A 3000 lb car is to be slowed from 220 mph to 50 mph in 4 seconds.  Assume a drag force proportional to speed.  What is the value of k, and how far will the car travel while being slowed?

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Question:  3.6.6.  A vertical projectile of mass m has initial velocity v_0 and drag force of magnitude k v.  How long after being fired will it reach its maximum height?

If the projectile has mass .12 grams and after being fires straight upward at 80 meters / second reaches its maximum height after 2.5 seconds, then what is the value of k?

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Question:  3.6.10.  A 82 kg skydiver falls freely for 10 seconds then opens his chute.  He reaches the ground 4 seconds later.  Assume air resistance is proportional to speed, and assume that with this chute a 90 kg would reach a terminal velocity of 5 m / s. 

At what altitude was the parachute opened?

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