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/s^2)
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 o f 77 ft/sec meet the dept need? explain
To determine if a pump with a velocity of 77 ft/sec will meet the needs of the Jackson Fire Department, we can compare the given velocity with the velocity equation and find the maximum height the pump can reach. If the maximum height is greater than or equal to 90 ft, then the pump will meet the department's needs.
Given:
v = 77 ft/sec (velocity)
g = 32 ft/sec^2 (acceleration due to gravity)
Using the velocity equation:
v = √(2hg)
We need to solve this equation for h (maximum height). Rearranging the equation, we get:
h = v^2 / (2g)
Plugging in the values:
h = (77 ft/sec)^2 / (2 * 32 ft/sec^2)
h = 5929 ft^2/sec^2 / 64 ft/sec^2
h ≈ 92.64 ft
Hence, the maximum height the pump can reach is approximately 92.64 ft. Since this is greater than the 90 ft requirement, the pump will indeed meet the needs of the Jackson Fire Department.