A fire hose ejects a stream of water at an angle of 36.4 ° above the horizontal. The water leaves the nozzle with a speed of 20.1 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

Question

A fire hose ejects a stream of water at an angle of 36.4 ° above the horizontal. The water leaves the nozzle with a speed of 20.1 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

Answer 1

Vo = 20.1m/2[36.4o]

Xo = 20.1*cos36.4o = 16.18 m/s.
Yo = 20.1*sin36.4o = 11.93 m/s.

Y = Yo + g*t = 0 @ max. ht.
11.93 + (-9.8)*t = 0
-9.8t = -11.93
Tr = 1.22 s. = Rise time.

d = Xo * Tr = 16.18m/s * 1.22s = 19.7 m.

Answer 2

Airplane flight recorders must be able to survive catastrophic crashes. Therefore, they are typically encased in crash-resistant steel or titanium boxes that are subjected to rigorous testing. One of the tests is an impact shock test, in which the box must survive being thrown at high speeds against a barrier. A 41 kg box is thrown at a speed of 220 m/s and is brought to a halt in a collision that lasts for a time of 6.5 ms. What is the magnitude of the average net force that acts on the box during the collision?

Round answer to nearest 100,000's place
i.e. 123456789 would therefore be 123500000

Answer 3

To find the horizontal distance from the building where the water hits the highest point, you need to calculate the range of the water projectile. The range can be determined using the following formula:

Range = (velocity^2 * sin(2θ))/g

Where:
- Velocity is the initial velocity of the water (in this case, 20.1 m/s)
- θ is the launch angle (36.4 °)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Substituting these values into the formula:

Range = (20.1^2 * sin(2 * 36.4))/9.8

First, calculate the value inside the sine function:

2 * 36.4 = 72.8

sin(72.8) ≈ 0.947

Now, substitute this value back into the range formula:

Range = (20.1^2 * 0.947)/9.8

Next, calculate the square of the velocity:

20.1^2 = 404.01

Now substitute all the values into the range formula:

Range = (404.01 * 0.947)/9.8

Finally, solve for the range:

Range ≈ 38.96 meters

So, the fire hose should be located approximately 38.96 meters away from the building to hit the highest possible fire.