Respuesta :
The air temperature if you are 700 m from the ship is 32°C
Further explanation
Acceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem !
Given:
time intervals = t = 2 s
distance = d = 700 m
Unknown:
air temperature = θ = ?
Solution:
At first we calculate the speed of sound at that time :
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{700}{2}[/tex]
[tex]\boxed {v = 350 ~ m/s}[/tex]
Finally, the temperature at that time can be calculated using the following formula :
[tex]v = 331 + 0.6 ~ \theta[/tex]
[tex]350 = 331 + 0.6 ~ \theta[/tex]
[tex]0.6 ~ \theta = 350 - 331[/tex]
[tex]0.6 ~ \theta = 19[/tex]
[tex]\theta = 19 \div 0.6[/tex]
[tex]\large {\boxed {\theta \approx 32^o ~ C} }[/tex]
Learn more
- Velocity of Runner : https://brainly.com/question/3813437
- Kinetic Energy : https://brainly.com/question/692781
- Acceleration : https://brainly.com/question/2283922
- The Speed of Car : https://brainly.com/question/568302
Answer details
Grade: High School
Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate
The temperature of the air is [tex]\boxed{31.67^\circ {\text{ C}}}[/tex].
Further Explanation:
The velocity of an object can be defined as the rate at which the object changes its distance.
Velocity is the vector quantity has some magnitude and some direction represented in the coordinates system on the [tex]x[/tex], [tex]y[/tex] and [tex]z[/tex]-axis.
The speed of the sound is depends on the medium in which sound travelling. The speed of the sound is higher in the solid medium and lowest speed in gases medium.
The speed of sound is depending on the temperature and pressure of the air. The high pressure can make particles to come closer to each other and increases the speed of sound and low pressure make particles to move away from each other. The strength of the interaction between the particles present in the air is affected by the temperature.
Given:
The time is [tex]2\text{ s}[/tex].
The total distance is [tex]700\text{ m}[/tex].
Concept:
The expression for the velocity can be written as:
[tex]\fbox{\begin\\v = \dfrac{d}{t}\end{minispace}}[/tex]
Here, [tex]v[/tex] is the velocity of the sound, [tex]d[/tex] is the distance and [tex]t[/tex] is the time.
Substitute [tex]2{\text{ s}}[/tex] for [tex]t[/tex] and [tex]700{\text{ m}}[/tex] for [tex]d[/tex] in the above equation.
[tex]\begin{aligned} v&=\frac{{700{\text{ m}}}}{{2{\text{ s}}}}\hfill\\&=350{\text{ m/s}} \hfill\\ \end{aligned}[/tex]
The expression for the speed of sound in air is written as:
[tex]\fbox{\begin\\v=v_{o}+0.6T\end{ minispace}}[/tex]
Here, [tex]{v_o}[/tex] is the velocity of the sound in medium at given temperature, [tex]T[/tex] is the tempura of the air in degree Celsius.
The speed of sound at [tex]0^\circ {\text{ C}}[/tex] is [tex]331{\text{ m/s}}[/tex].
Substitute [tex]331{\text{ m/s}}[/tex] for [tex]{v_o}[/tex], [tex]350{\text{ m/s}}[/tex] for [tex]v[/tex] in the above equation.
[tex]\begin{aligned}350{\text{ m/s}}&=331{\text{ m/s}} + \left( {0.6T} \right){\text{m/s}} \cdot ^\circ C \hfill\\0.6T&=19{\text{ m/s}}\hfill\\T&=\frac{{19{\text{ m/s}}}}{{0.6{\text{ m/s}}\cdot^\circ C}}\hfill\\&=31.67^\circ {\text{ C}}\hfill\\ \end{aligned}[/tex]
Therefore, the temperature of the air is [tex]\boxed{31.67^\circ {\text{ C}}}[/tex].
Learn more:
1. Sound properties https://brainly.com/question/1621941
2. Factors affect the speed of sound https://brainly.com/question/12343551
3. Properties of sound remain the same https://brainly.com/question/9898147
Answer Details:
Grade: Middle school
Subject: Physics
Chapter: Sound
Keywords:
Condensed, steam, expelled, ship’s whistle, 2 s, hear, sound, air temperature, 700 m, 31.67 deg C.
