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1 year ago

8

Whitney kicks a football off the ground. The height, h , in feet, of the football above the ground after t seconds is given by h

( t ) = − 8 t 2 + 32 t . How many seconds after the football is kicked does it hit the ground for the first time?

1 answer:

malfutka [58]1 year ago

5 0

Answer:

<em>after 4seconds</em>

Step-by-step explanation:

Given the height, h , in feet, of the football above the ground after t seconds expressed by h ( t ) = − 8 t^2 + 32 t, the height of the ball on the ground is 0feet.

Substitute h(t) = 0 into the expression and calculate t;

h ( t ) = − 8 t^2 + 32 t

0 = − 8 t^2 + 32 t

8t² = 32t

8t = 32

Divide both sides by 8

8t/8 = 32/8

<em>t = 4s</em>

<em>Hence the football hits the ground after 4seconds</em>

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Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

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The radius is half the diameter. The diameter of the sphere is 10, thus:

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5^3 = 5*5*5 = 25*5 = 125

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The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

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$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

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Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

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I'll now divide both the numerator and the denominator by 25 to simplify the expression:

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