Question

A football is kicked at 40 yards away from goal post that is 10 feet high.its path is modeled by y=-0.03^2+1.6x where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet. Does the football go over the goal post ? How far above or below the goal post is the football?

Answer 1

Goes above the post by 6ft.

Explanation:

1. The ball does go above the post. It goes 6 ft above the post.

2.Since the path is modeled by this equation: y = -0.03x^2 + 1.6x, We change x for the distance the ball needs to travel, which is 40 yards. So we plug 40 in: -0.03(40)^2 + 1.6(40). We simplify to get: -48 + 64 = 16. Because the ball is 16 feet in the air, we can assume that it is above the post, which is 10 feet. And we can also assume, by subtracting 16 - 10, that the ball went over the post by 6ft

Answer 2

Since we have the equation that models the movement of the ball, we simply need to replace the corresponding values in the equation.
Althought there seems to be an X missing, so it should be
y=-0.03*x^2+1.6x
like this, the graph should be as the picture shows.
We can immediately see in the picture that the football does go over the goal post, let's see how much, by replacing the values:

`y=-0.03*40^2+1.6*40=-0.03*1600+64=16`
since the pole is 10 ft high, the ball is 6 above the post