The flight of a soccer ball is modeled by h(t) = –16t2 + 40t What is the maximum height the ball reached?

How long did it take the ball to reach its maximum height?

How long did it take for the ball to fall back to the ground?

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Ответ:

nockturnal1993

07.02.2021

Mathematics

I am getting 7 as the value of b. I do not believe 4 is a correct answer!

Here's why:

General equation of a circle in the xy plane

(x-c_x)^2+(y-x_y)^2=r^2

with $c_x\,\,\mbox{and}\,\,c_y$ being the x,y coordinates of the center.

The center point can be determined from the two endpoints of the diameter because the line segment is horizontal, so we just find the center of the x coordinates of the two points:

$c_x = -2+\frac{|8-(-2)|}{2}=3\\c_y = 3$

and the radius r = diameter/2 = 8-(-2)/2 = 5

so we have

(x-3)^2+(y-3)^2=5^2

Given a point on the circle (0,b) with b>0:

$(0-3)^2+(b-3)^2=5^2\\9+(b-3)^2 = 25\\(b-3)^2 = 16\\b=7$

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The flight of a soccer ball is modeled by h(t) = –16t2 + 40t What is the maximum height the ball reached? How long did it take the ball to reach its maximum height? How long did it take for the ball to fall back to the ground?