October 16th, 2010, 01:03 PM  #1 
Newbie Joined: Oct 2010 Posts: 2 Thanks: 0  free falling question
I have this free falling question and it would be greatly appreciated if someone could help me 1) Problem: Wyle Coyote was chasing a roadrunner in his acme homemade helicopter. Unfortunately it took him so long to catch up to the roadrunner that he ran out of gas. When he ran out of gas he was hovering 400 feet above the ground looking for the roadrunner. At that moment, the coyote and the helicopter proceeded to fall freely to earth. So the formula in the case of the coyote is h(t)=40016t^2. 1. What is the height of the coyote 3 seconds after he starts to drop? 2. How far has he fallen during those 3 seconds? 3. What is his average speed during those 3 seconds? 4. How long will it take from the time the coyote starts to fall until he hits the ground? 5. How far does the coyote fall during the last second before he hits the ground? 6. Based on the formula how might you find the coyote's speed at the exact moment he hits the ground? 
October 16th, 2010, 04:05 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: free falling question
1. What is the height of the coyote 3 seconds after he starts to drop? Here, t = 3 seconds, thus h(3) = 400  16(3)² = 256 ft. 2. How far has he fallen during those 3 seconds? ?h = h(0)  h(3) = 400  256 = 144 ft. 3. What is his average speed during those 3 seconds? v = d/t = (144 ft)/(3 s.) = 48 ft./s. 4. How long will it take from the time the coyote starts to fall until he hits the ground? 0 = 400  16t² t² = 25 t = 5 s 5. How far does the coyote fall during the last second before he hits the ground? h(4) = 400  16(4)² = 144 ft. 6. Based on the formula how might you find the coyote's speed at the exact moment he hits the ground? dh/dt = v(t) = 32t ?v(5)? = 160 ft./s. 

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