1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ira Lisetskai [31]
3 years ago
9

A firefighter mounts the nozzle of his fire hose a distance 36.9 m away from the edge of a burning building so that it sprays fr

om ground level at a 45° angle above the horizontal. After quenching a hotspot at a height of 8.85 m, the firefighter adjusts the nozzle diameter so that the water hits the building at a height of 17.9 m. By what factor was the nozzle diameter changed? Assume that the diameter of the hose stays the same, and treat the water as an ideal fluid.

Physics
2 answers:
Kryger [21]3 years ago
6 0

The nozzle diameter changed by a factor of 0.907

\texttt{ }

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

\large {\boxed {a = \frac{v - u}{t} } }

\large {\boxed {d = \frac{v + u}{2}~t } }

<em>a = acceleration (m / s²)v = final velocity (m / s)</em>

<em>u = initial velocity (m / s)</em>

<em>t = time taken (s)</em>

<em>d = distance (m)</em>

Let us now tackle the problem!

\texttt{ }

<u>Given:</u>

horizontal distance = x = 36.9 m

angle of projection = θ = 45°

initial height = y₁ = 8.85 m

final height = y₂ = 17.9 m

<u>Asked:</u>

ratio of nozzle diameter = d₂ : d₁ = ?

<u>Solution:</u>

<em>The motion of the water is a </em><em>parabolic motion.</em>

<em>Firstly, we will calculate the time taken for the water to reach the hotspot:</em>

x = (u \cos \theta) t

t = x \div ( u \cos \theta )

t = x \div ( u \cos 45^o )

\boxed {t = \frac{\sqrt{2}x}{u}}

\texttt{ }

<em>Next , we could calculate the initial speed (u) of the water as it leaves the nozzle:</em>

y = (u \sin \theta) t - \frac{1}{2}gt^2

y = (u \sin 45^o)( \frac{\sqrt{2}x}{u} ) - \frac{1}{2}g ( \frac{\sqrt{2}x}{u} )^2

y = x - \frac{gx^2}{u^2}

\frac{gx^2}{u^2} = x - y

u^2 = \frac{gx^2}{x - y }

u = \sqrt{ \frac{gx^2}{x - y } }

\boxed {u = x \sqrt{ \frac{g}{x - y} }}

\texttt{ }

<em>Finally , we could find the ratio of the diameter by using </em><em>Continuity Equation</em><em> as follows:</em>

u_1 A_1 = u_2 A_2

u_1 \frac{1}{4} \pi (d_1)^2 = u_2 \frac{1}{4} \pi (d_2)^2

(d_2)^2 : (d_1)^2 = u_1 : u_2

(d_2)^2 : (d_1)^2 = x \sqrt{ \frac{g}{x - y_1} } : x \sqrt{ \frac{g}{x - y_2} }

(d_2)^2 : (d_1)^2 = \sqrt { x - y_2 } : \sqrt { x - y_1}

\frac {d_2}{d_1} = \sqrt[4] { \frac {x - y_2} {x - y_1} }

\frac {d_2}{d_1} = \sqrt[4] { \frac {36.9 - 17.9} {36.9 - 8.85} }

\frac {d_2}{d_1} \approx 0.907

d_2 \approx 0.907 \times d_1

\texttt{ }

<h3>Learn more</h3>
  • Velocity of Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302

\texttt{ }

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

inysia [295]3 years ago
3 0

Answer:

diameter is decreased by factor 0.91

Explanation:

As we know by the equation of trajectory

y = xtan\theta - \frac{gx^2}{2v^2cos^2\theta}

here as per first given situation we know that

x = 36.9 m

y = 8.85 m

\theta = 45^0

now from above equation we have

8.85 = 36.9 tan45 - \frac{(9.8)(36.9)^2}{2(v^2)cos^245}

8.85 = 36.9 - \frac{13343.8}{v^2}

\frac{13343.8}{v^2} = 28.05

v = 21.8 m/s

now similarly after nozzle is adjusted we have

y = 17.9 m

x = 36.9 m

\theta = 45^0

now again from equation we have

17.9 = 36.9 tan45 - \frac{(9.8)(36.9)^2}{2(v'^2)cos^245}

17.9 = 36.9 - \frac{13343.8}{v'^2}

\frac{13343.8}{v'^2} = 19

v' = 26.5 m/s

Now by equation of continuity we can find the change in diameter

as we know that

A_1v_1 = A_2v_2

now we have

\pi d_1^2 v_1 = \pi d_2^2 v_2

d_1^2 (21.8) = d_2^2(26.5)

\frac{d_1}{d_2} = \sqrt{\frac{26.5}{21.8}}

\frac{d_1}{d_2} = 1.10

so we have

\frac{d_2}{d_1} = 0.91

so diameter is decreased by factor of 0.91

You might be interested in
you are piloting a small plane and you want to reach an airport 450 km due south in 3.0 h a wind is blowing from the west 50.0 k
alex41 [277]

Answer:

You should choose airspeed 158.11 km/h at 18.4° west of south

Explanation:

The distance to the air port is 450 km due to south

You should to reach the airport in 3 hours

→ Velocity = distance ÷ time

→ Distance = 450 km , time = 3 hours

→ The velocity of your plane = 450 ÷ 3 = 150 km/h due to south

A wind is blowing from west 50 km/h

We need to know what heading and airspeed you should choose to

reach your destination

At first we must find the resultant velocity of your plane and the wind

The south and west are perpendicular, then the resultant velocity is

→ v_{R}=\sqrt{(v_{p})^{2}+(v_{w})^{2}}

→ v_{p}=150 km/h ,  v_{w}=50 km/h

→ v_{R}=\sqrt{(150)^{2}+(50)^{2}}=158.11 km/h

To cancel the velocity of the wind, the pilot should maintain the velocity

of the plane at 158.11 km/h

The direction of the velocity is the angle between the resultant velocity

and the vertical (south)

→ The direction of the velocity is tan^{-1}\frac{50}{150}=18.4°

The direction of the velocity is 18.4° west of south

<em>You should choose airspeed 158.11 km/h at 18.4° west of south</em>

8 0
3 years ago
Which statements provides evidence that the earth revolves around the sun
Aloiza [94]

Answer:

Different star constellations are visible from Earth at different seasons of the year.

Explanation:

The reason the fact that we can see different constellations in the sky during different seasons on earth is the most compelling reason we travel around the sun is because if the sun travelled around the earth, certain constellations would only be visible in certain places. You’d have to travel to see certain ones.

However, you don’t have to do that because we travel around the sun, therefore travelling around other stars too.

4 0
3 years ago
I need help with 5 please and thank you
Likurg_2 [28]

Answer: A

Explanation:

7 0
3 years ago
Plzz Help worth 10 points!!! which statement about energy transformations is not true?
EleoNora [17]
I think it could be A
6 0
3 years ago
Read 2 more answers
How far does a car travel in 90 seconds if it’s traveling 55 m/s? Show equation
podryga [215]

You just said the car is traveling at the speed of 55 m/s.  If I understand this  correctly, that means the car will cover:

55 meters in the first second,

55 meters in the 2nd second,

55 meters in the 3rd second,

55 meters in the 4th second,

55 meters in the 5th second,

.

.

.

55 meters in the 87th second,

55 meters in the 88th second,

55 meters in the 89th second, and

55 meters in the 90th second.

That's 55 meters 90 times.  If you just move these words around a little bit, it says "90 times 55 meters" . . . a pretty simple arithmetic problem.

The equation is . . . <em>Distance = (55 m/s) times (time, in seconds)</em> .

I get <em>4,953 meters</em>.  You should check me on this.

8 0
3 years ago
Other questions:
  • How many grams of nitrogen gas are needed to produce 34 g of ammonia
    9·1 answer
  • PNEWTON<br> What is the ist law of motion?
    12·1 answer
  • Elabora una tabla, como la del ejemplo, con los resultados obtenidos en los test que desarrollaste en actividades anteriores. Lu
    9·1 answer
  • A small cube of metal measures 19.0 mm on a side and weighs 79.6 g. What is the density of the metal in g/cm3?
    14·1 answer
  • How can resistance be useful and where can they be useful?
    11·1 answer
  • A 5 kilogram block is dropped from a height of 3 meters and falls straight to the ground. What is the work done by the force of
    5·1 answer
  • What is the smallest particle of an element that still retains of that element
    9·1 answer
  • List at least types of motion​
    9·2 answers
  • When you jump, you push down on the earth and it pushes back up against you. The earth pushing up against you is what causes you
    9·1 answer
  • I need help with a physics worksheet about Newtons Laws.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!