Question

A fountain on a lake sprays water in a parabolic arch modeled by the equation y = −0.4x2 + 3x, where y is the height in feet and x is the horizontal distance. A beam of light is passed through the fountain to create a rainbow effect. If the beam is directed at an angle modeled by the equation -2.2x + 4.9y = 8.18, at what distance from the ground will the beam first touch the water spray?

Answer 1

Hello,

y=-1.4x²+3x
y=2.2/4.9 x +8.18/4.9

-0.4x²+3x=2.2/4.9 x +8.18/4.9

==>1.96 x² -12.5x +8.18=0
Δ=92.1188....=9.597...²

x=(12.5-9.597...)/(2*1.96)=0.7403433....
=>y=-0.4*0.7403...²+3*0.7403...=2.00178682...

Answer: 2.001... ft