Question 241575: A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)=-16t2+30, where t is time, in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)=-8+15. Can the gull catch the crab before the crab hits the water? justify your answer. If so, find the time it is caught and the distance above the water at that time.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)=-16t2+30, where t is time, in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t)=-8t+15. Can the gull catch the crab before the crab hits the water? justify your answer. If so, find the time it is caught and the distance above the water at that time.
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That is a neat problem.
Find the intersection of the gull-line with the crab parabola.
-8t+15 = -16t^2+30
16t^2-8t-15 = 0
(4t-5)(4t+3) = 0
Positive solutiion:
t = 5/4 seconds (time at which the gull and the crab meet)
g(5/4) = -8(5/4)+15 = 5 ft. (height at which the gull and the crab meet)
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Cheers,
Stan H.
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