Question

A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the equation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?

Answer 1

See the attached figure.

Water model ⇒⇒⇒ y = -0.3 x² + 3x        ( blue graph )
Light model   ⇒⇒⇒ -2x + 5.5 y = 19.5    ( red graph )
The intersection between the two models A and B
A = ( 1.657 , 4.148 )
B = ( 7.13 , 6.138 )

B is at a higher level than point A

The distance from the ground level to point A = y-coordinate of point A
                                                                        = 4.148