The recoil speed of the cannon is 3 m/s.
<u>Explanation:</u>
Law of conservation of momentum is used to find the recoil speed of the cannon.
m₁v₁ = -m₂v₂
m₁= mass of clown = 100 kg
v₁ = speed of the clown = 15 m/s
m₂= mass of the cannon = 500 kg
v₂ = speed of the cannon = ?
Plugin the values, we will get,
v₂ = m₁v₁ / -m₂ = -100×15/ 500 = -1500 / 500 = 3 m/s
So the recoil speed of the cannon is 3 m/s.
<u></u>
Answer: The multiplication factor is 72.136 cm. This will give you the unit conversion when multiplied with 28.4 inch
Explanation:
1 inch = 2.54 cm
28.4 inches = x cm
Xcm= (28.4 inches × 2.54cm)/1 inch
X= 72.136
Answer: The frequency is inversely related to wavelength in electromagnetic wave.
Explanation:
Relationship between the frequency and wavelength of wave is given by the equation:
![\nu=\frac{c}{\lambda}](https://tex.z-dn.net/?f=%5Cnu%3D%5Cfrac%7Bc%7D%7B%5Clambda%7D)
where,
= Frequency of the wave
c = speed of light = ![3\times 10^8m/s](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E8m%2Fs)
= Wavelength of the wave
From the above relation, it is visible that frequency is inversely related to the wavelength of the wave.
Higher the frequency, low will be the wavelength of the wave and vice-versa.
I'll just find out the path difference between the waves at the starting point. At infinity, the path difference will be zero because the observer will be infinitely far away from both. As the observer goes farther, the path difference keeps reducing till it reaches zero as the observer reaches infinity.
<span>Path difference at starting point = Distance from lower speaker - Distance from upper speaker = √((3)² + (2.5)²) - 2.5 = 1.405 m </span>
<span>Now to find wavelength. </span>
<span>Speed of sound in air at 20 degrees C = 343 m/s </span>
<span>Wavelength = 343 / 686 = 0.5 m </span>
<span>Destructive interference occurs when path difference = (2n + 1)λ/2 where n is an integer. </span>
<span>Maximum n possible can be found by, </span>
<span>(2n + 1)λ/2 < 1.405 </span>
<span>(2n + 1) < (1.4)(2) / (0.5) </span>
<span>2n < 5.6 - 1 </span>
<span>2n < 4.6 </span>
<span>n < 2.3 </span>
<span>So, we have 3 values of n, 0, 1 and 2. </span>
<span>Path differences are, λ/2, 3λ/2 and 5λ/2 which have values 0.25 m , 0.75 m and 1.25 m </span>
<span>But the question asks for distance from starting point. (sheesh!!) </span>
<span>Lets say the observer walked x distance. </span>
<span>Path difference = √((3)² + (2.5 + x)²) - (2.5 + x) </span>
<span>Equate this expression to the values obtained above to get the different values of x. </span>
Change in volume = mass x coefficient of linear expansion x change in temperature
.002 x .0001802 x 30 = .000010812
initial volume + change in volume = Final volume
.002 + .000010812 = .002010812 m cubed