Answer:
![\theta=39.49^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D39.49%5E%7B%5Ccirc%7D)
Explanation:
Maximum height of the pumpkin, ![H_{max}=9.99\ m](https://tex.z-dn.net/?f=H_%7Bmax%7D%3D9.99%5C%20m)
Initial speed, v = 22 m/s
We need to find the angle with which the pumpkin is fired. the maximum height of the projectile is given by :
![H_{max}=\dfrac{v^2\ sin^2\theta}{2g}](https://tex.z-dn.net/?f=H_%7Bmax%7D%3D%5Cdfrac%7Bv%5E2%5C%20sin%5E2%5Ctheta%7D%7B2g%7D)
On rearranging the above equation, to find the angle as :
![\theta=sin^{-1}(\dfrac{\sqrt{2gH_{max}}}{v})](https://tex.z-dn.net/?f=%5Ctheta%3Dsin%5E%7B-1%7D%28%5Cdfrac%7B%5Csqrt%7B2gH_%7Bmax%7D%7D%7D%7Bv%7D%29)
![\theta=sin^{-1}(\dfrac{\sqrt{2\times 9.8\times 9.99}}{22})](https://tex.z-dn.net/?f=%5Ctheta%3Dsin%5E%7B-1%7D%28%5Cdfrac%7B%5Csqrt%7B2%5Ctimes%209.8%5Ctimes%209.99%7D%7D%7B22%7D%29)
![\theta=39.49^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D39.49%5E%7B%5Ccirc%7D)
So, the angle with which the pumpkin is fired is 39.49 degrees. Hence, this is the required solution.
Explanation:
Earth rotates in prograde mation.As viewed from the north pole star Polaris.Earth turns counterclockwise,, the north pole is point in the northern,, Hemisphere where Earth's Axis of rotation meets it's surface
Power is the energy transferred or "WORK DONE" in one second
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.