The path of a basketball foul shot is modelled by the relation h=-0.44d*2+4.4d+7, where h is the height in feet and d is the horizontal distance in feet. At what height is the ball released? What was the maximum height the ball reached? The centre of the basket is 14 feet away at a height of 10 feet. Assuming that the shot was straight, could the ball pass through the hoop?
what is h when d=0?
As you know the vertex of a parabola is where d = -b/2a = -4.4/-.88
So, figure h for that value of d.
What is h when d=14? Or, how far away is the ball when h=0 (it hits the floor)?
To find the height at which the ball is released, we need to substitute the value of d=0 into the equation h=-0.44d^2+4.4d+7.
Substituting d=0:
h = -0.44(0)^2 + 4.4(0) + 7
h = 0 + 0 + 7
h = 7
Therefore, the ball is released at a height of 7 feet.
To find the maximum height reached by the ball, we need to determine the vertex of the parabolic equation h=-0.44d^2+4.4d+7. The vertex of a parabola can be found using the formula d=-b/2a, where a and b are coefficients of the quadratic equation.
For our equation h=-0.44d^2+4.4d+7, the coefficient of d^2 is -0.44 and the coefficient of d is 4.4. Plugging these values into the formula, we get:
d = -4.4 / (2 * (-0.44))
d = -4.4 / (-0.88)
d = 5
Substituting d=5 into the equation h=-0.44d^2+4.4d+7, we can find the maximum height reached by the ball:
h = -0.44(5)^2 + 4.4(5) + 7
h = -0.44(25) + 22 + 7
h = -11 + 22 + 7
h = 18
Therefore, the maximum height reached by the ball is 18 feet.
The center of the basket is located 14 feet away at a height of 10 feet. For the ball to pass through the hoop, its height should be equal to or greater than 10 feet when it reaches a horizontal distance of 14 feet.
To check if the ball can pass through the hoop, we substitute d=14 into the equation h=-0.44d^2+4.4d+7:
h = -0.44(14)^2 + 4.4(14) + 7
h = -0.44(196) + 61.6 + 7
h = -86.24 + 61.6 + 7
h = -17.64
Since the height at a horizontal distance of 14 feet is -17.64 feet, which is below the height of the hoop (10 feet), the ball cannot pass through the hoop.