When fighting a fire the velocity V of water being pumped into the air is modeled by the function v=�ã2hg, where h represents the maximum height of the water and g represents the acceleration due to gravity (32 ft/s^2)

Question

Solve the function for h.
Would this be v=�ã(2h*32)

The Jackson Fire dept must purchase a pump that will propel water 90ft into the air. will a pump advertised to project water with a velocity of 77 ft/sec meet the dept need? explain

Answer 1

The square root symbol did not show using alt+251.
v=�ã2hg

Answer 2

The alt+251 would probably work for Microsoft Word or other word processors. Here the symbols require unicode sequences.
See for example:
http://tlt.its.psu.edu/suggestions/international/bylanguage/mathchart.html

You can show the square-root symbol using the following letter sequence (skip the spaces in-between):
& r a d i c ;
to get the symbol √.

Answer 3

Thank you MathMate for the instructions on the √

Answer 4

"Solve the function for h. "
requires that h will be the dependent variable (similar to y) in terms of v.

Given:
v=√(2gh)
square both sides:
v² = 2gh
solve for h as a function of g:
h(v)=v²/(2g)

For the new purchase,
h(77)=77²/(2*32.2)
= 92.1 ft.
> minimum requirement of 90 ft.

Note: the calculated maximum h will be attained if the water is aimed at 45° with the horizontal, and without air-resistance.