Explanation:
Given that,
A ball is tossed straight up with an initial speed of 30 m/s
We need to find the height it will go and the time it takes in the air.
At its maximum height, its final speed, v = 0 and it will move under the action of gravity. Using equation of motion :
v = u +at
Here, a = -g
v = u -gt
i.e. u = gt
![t=\dfrac{u}{g}\\\\t=\dfrac{30\ m/s}{9.8\ m/s^2}\\\\t=3.06\ s](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bu%7D%7Bg%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B30%5C%20m%2Fs%7D%7B9.8%5C%20m%2Fs%5E2%7D%5C%5C%5C%5Ct%3D3.06%5C%20s)
So, the time for upward motion is 3.06 seconds. It means that it will in air for 3.06×2 = 6.12 seconds
Let d is the maximum distance covered by it.
![d=ut-\dfrac{1}{2}gt^2](https://tex.z-dn.net/?f=d%3Dut-%5Cdfrac%7B1%7D%7B2%7Dgt%5E2)
Putting all values
![d=30(3.06)-\dfrac{1}{2}\times 9.8\times (3.06)^2\\\\d=45.91\ m](https://tex.z-dn.net/?f=d%3D30%283.06%29-%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%209.8%5Ctimes%20%283.06%29%5E2%5C%5C%5C%5Cd%3D45.91%5C%20m)
Hence, it will go to a height of 45.91 m and it will in the air for 6.12 seconds.
Answer:
The observer detects light of wavelength is 115 nm.
(b) is correct option
Explanation:
Given that,
Wavelength of source = 500 nm
Velocity = 0.90 c
We need to calculate the wavelength of observer
Using Doppler effect
![\lambda_{o}=\sqrt{\dfrac{1-\beta}{1+\beta}}\lambda_{s}](https://tex.z-dn.net/?f=%5Clambda_%7Bo%7D%3D%5Csqrt%7B%5Cdfrac%7B1-%5Cbeta%7D%7B1%2B%5Cbeta%7D%7D%5Clambda_%7Bs%7D)
Where, ![\beta=\dfrac{c}{v}](https://tex.z-dn.net/?f=%5Cbeta%3D%5Cdfrac%7Bc%7D%7Bv%7D)
![\lambda_{o}=\sqrt{\dfrac{c-0.90c}{c+0.90c}}\times500\times10^{-9}](https://tex.z-dn.net/?f=%5Clambda_%7Bo%7D%3D%5Csqrt%7B%5Cdfrac%7Bc-0.90c%7D%7Bc%2B0.90c%7D%7D%5Ctimes500%5Ctimes10%5E%7B-9%7D)
![\lambda_{o}=115\ nm](https://tex.z-dn.net/?f=%5Clambda_%7Bo%7D%3D115%5C%20nm)
Hence, The observer detects light of wavelength is 115 nm.
Answer:
The possible range of wavelengths in air produced by the instrument is 7.62 m and 0.914 m respectively.
Explanation:
Given that,
The notes produced by a tuba range in frequency from approximately 45 Hz to 375 Hz.
The speed of sound in air is 343 m/s.
To find,
The wavelength range for the corresponding frequency.
Solution,
The speed of sound is given by the following relation as :
![v=f_1\lambda_1](https://tex.z-dn.net/?f=v%3Df_1%5Clambda_1)
Wavelength for f = 45 Hz is,
![\lambda_1=\dfrac{v}{f_1}](https://tex.z-dn.net/?f=%5Clambda_1%3D%5Cdfrac%7Bv%7D%7Bf_1%7D)
![\lambda_1=\dfrac{343}{45}=7.62\ m](https://tex.z-dn.net/?f=%5Clambda_1%3D%5Cdfrac%7B343%7D%7B45%7D%3D7.62%5C%20m)
Wavelength for f = 375 Hz is,
![\lambda_2=\dfrac{v}{f_2}](https://tex.z-dn.net/?f=%5Clambda_2%3D%5Cdfrac%7Bv%7D%7Bf_2%7D)
![\lambda_2=\dfrac{343}{375}=0.914\ m/s](https://tex.z-dn.net/?f=%5Clambda_2%3D%5Cdfrac%7B343%7D%7B375%7D%3D0.914%5C%20m%2Fs)
So, the possible range of wavelengths in air produced by the instrument is 7.62 m and 0.914 m respectively.
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