Sara jumps off a diving board that is 6 feet above the surface of the water her height above the surface of the water h in feet is a function of time t in seconds as modeled by the quadratic function h (t) = - 2t^2 + t + 6 how many seconds did it take sara to hit the surface of the water after she jumped off the diving board

Question

Mathematics

Jude Levy

13 March, 14:34

Sara jumps off a diving board that is 6 feet above the surface of the water her height above the surface of the water h in feet is a function of time t in seconds as modeled by the quadratic function h (t) = - 2t^2 + t + 6 how many seconds did it take sara to hit the surface of the water after she jumped off the diving board

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Tapia · Answer 1

Well when she hits the water h=0 so

2t^2-t-6=0 factor

2t^2-4t+3t-6=0

2t (t-2) + 3 (t-2) = 0

(2t+3) (t-2) = 0, since t>0

t=2 seconds ...

However it should be noted that h (t) = - 2t^2+t+6 implies that

v (t) = dh/dt=-4t+1 and

a (t) = dv/dt=-4

Since this is a free fall equation, this would suggest that the acceleration due to gravity is - 4, whether that is supposed to be - 4ft/s^2 or - 4m/s^2, it certainly is not on this planet! : D If it is - 4ft/s^2 it could be on the Moon or if it is - 4m/s^2 it could be on Mars.