Question 520741
When fighting a fire, the velocity v of water being pumped into the air is modeled by the function v= √2hg, where h represents the maximum height of the water and g represents the acceleration due to gravity (32 ft/s2).
:
The Islip Fire Department must purchase a pump that will propel water 90 feet into the air.
 Will a pump that is advertised to project water with a velocity of 77 feet per second meet the fire departments need? EXPLAIN mathematically and verbally.
:
Find the velocity required, replace h with 90 ft, g with 32 ft/s
{{{v = sqrt(2*90*32)}}}
v = 75.86 ~ 76 ft/sec
therefore a pump with a 77 ft/sec will just do it
:
Find the actual height (h) that a pump with 77 ft/s is able accomplish
{{{sqrt(2*h*32)}}} = 77
{{{sqrt(64h)}}} = 77
square both sides
64h = 77^2
64h = 5929
h = {{{5929/64}}}
h = 92.6 ft