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Reil [10]
3 years ago
5

Determine the speed of sound in air at 300 K. Also determine the Mach number of an aircraft moving in the air at a velocity of 3

00 m/s. The gas constant of air is R = 0.287 kJ/kg·K. Its specific heat ratio at room temperature is k = 1.4.
Physics
1 answer:
amm18123 years ago
5 0

Answer:

c_3_0_0_K=347.19m/s

M=0.864

Explanation:

The speed of sound in the air increases 0.6 m / s for every 1 ° C increase in temperature.  An approximate speed can be calculated using the following empirical formula:

c=331.5+0.6\vartheta

Where:

\vartheta=T-273.15K\\\\

A more exact equation, usually referred to as adiabatic velocity of sound, is given by the following formula:

c=\sqrt{k*R*T}

Where:

R= Gas\hspace{3}constant\hspace{3}of\hspace{3}air=0.287kJ/kg*K=287J/kg*K\\k=Specific\hspace{3}heat\hspace{3}ratio=1.4\\T=Temperature=300K

Hence:

c=\sqrt{(287)*(1.4)*(300)} =347.1887095\approx347.19m/s

Now, the Mach number at which an aircraft is flying can be calculated by:

M=\frac{u}{c}

Where:

u= Velocity\hspace{3}of\hspace{3}the\hspace{3}moving\hspace{3}aircraft\\c= Speed\hspace{3}of\hspace{3}sound\hspace{3}at\hspace{3}the\hspace{3}given \hspace{3}altitude

Therefore:

M=\frac{300}{347.19} =0.8640833984\approx0.864

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14. a ball is thrown horizontally from the roof of a building 75 m tall with a speed of 4.6 m/s. a. how much later does the ball
Burka [1]

The time taken to hit the ground is 3.9 s, the range is 18m and the final velocity is 42.82 m/s

<h3>Motion Under Gravity</h3>

The motion of an object under gravity is the vertical motion of the object under the influence of acceleration due to gravity.

Given that a ball is thrown horizontally from the roof of a building 75 m tall with a speed of 4.6 m/s.

a. how much later does the ball hit the ground?

The time can be calculated by considering the vertical component of the motion with the use of formula below.

h = ut + 1/2gt²

Where

  • Height h = 75 m
  • Initial velocity u = 0 ( vertical velocity )
  • Acceleration due to gravity g = 9.8 m/s²
  • Time t = ?

Substitute all the parameters into the formula

75 = 0 + 1/2 × 9.8 × t²

75 = 4.9t²

t² = 75/4.9

t² = 15.30

t = √15.3

t = 3.9 s

b. how far from the building will it land?

The range can be found by using the formula

R = ut

Where u = 4.6 m/s ( horizontal velocity )

R = 4.6 × 3.9

R = 18 m

c. what is the velocity of the ball just before it hits the ground?

The final velocity will be

v = u + gt

v = 4.6 + 9.8 × 3.9

v = 4.6 + 38.22

v = 42.82 m/s

Therefore, the answers are 3.9 s, 18 m and 42.82 m/s

Learn more about Vertical motion here: brainly.com/question/24230984

#SPJ1

7 0
1 year ago
What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45.0° when it passes
sp2606 [1]
** Missing info: Lines per mm = 500 **

Ans: The wavelength is =  λ = 1414.21 nm

Explanation:
The formula for diffraction grading is:

dsinθ = mλ --- (1)

Where
d = 1/lines-per-meter = (1/500)*10^-3 = 2 * 10^-6
m = order = 1
λ = wavelength
θ = 45°

Plug in the values in (1):
(1) => 2*10^-6*sin(45°) = (1)λ
=> λ = 1414.21 nm
7 0
3 years ago
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