Question

Suppose the path of a baseball follows the path graphed by the quadratic function ƒ(d) = –0.6d2 + 5.4d + 0.8 where d is the horizontal distance the ball traveled in yards, and ƒ(d) is the height, in yards, of the ball at d horizontal yards. Find the total horizontal distance the ball traveled while in the air.
A. 8.22 yards
B. 8.46 yards
C. 9.51 yards
D. 9.15 yards

Answer 1

Answer:

The correct option D.

Step-by-step explanation:

The given function is

$f(d)=-0.6d^2+5.4d+0.8$

Where f(d) is the height of the ball at horizontal distance d.

Put f(d)=0, to find the distance where the ball touch the ground.

$0=-0.6d^2+5.4d+0.8$

Quadratic formula:

$d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using the quadratic formula we get

$d=\frac{-5.4\pm \sqrt{(5.4)^2-4(-0.6)(0.8)}}{2(-0.6)}$

$d=-0.146,9.146$

Therefore the ball is in air between d=-0.146 to d=9.146.

The distance can not be negative, therefore the ball remains in the air between d=0 to d=9.146.

$9.146\approx 9.15$

Therefore the correct option is D.