Answer to Question #134461 in Geometry for Joseph Se

Question

The Water Arc is a fountain that shoots water across the Chicago River from a water cannon. The path of the water can be approximated by the equation h = −0.006x2 + 1.2x + 10, where x is the horizontal distance, in feet, from the cannon and h is the height, in feet, of the water above the river. On one particular day, some people were walking along the opposite side of the river from the Water Arc when a pulse of water was shot in their direction. If the distance from the Water Arc to the people was 215 ft, did they get wet from the cannon's water?

A. Yes
B. No

Answer 1

Solution.

Find the distance (x) from the Water Arc to the place where the water jet falls into the river (where h=0):

$-0.006\cdot x^2+1.2\cdot x+10=0$ , where

$x=\frac{-1.2-\sqrt{1.2^2-4\cdot(-0.006)\cdot10}}{2\cdot(-0.006)}=208.012ft < 215ft$ - the water jet did not reach people (see plot).

Answer: B. No.