SOLUTION: h(t)= c-(d-4t)^2 At time t=0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the fun

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Question 389681: h(t)= c-(d-4t)^2
At time t=0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t= 2.5, what was the height, in feet, of the ball at time t = 1?
Answer by solver91311(24713) (Show Source):
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Expand the binomial:

Compare this to the standard form of the height function for a projectile near the surface of the Earth with respect to time:

By comparison you can see that the initial height, , must be equal to , and the initial velocity, .

We know that the maximum height is obtained at the time equal to the -coordinate of the vertex of the parabola that is the graph of the function. The -coordinate is found by:

but we were given that

From which we can deduce:

(verification left as an exercise for the student)

and then we can determine that

Next we were given that , but knowing that , we can deduce that:

Plug in the values:

And then do the arithmetic.

John

My calculator said it, I believe it, that settles it