Answer:
Step-by-step explanation:
Number 5 is third option
and number 6 is second option
Answer:
The plane travels at a speed of approximately 262.768 miles per hour.
Step-by-step explanation:
The absolute velocity of the plane (
) is the vectorial sum of vectors from engines (
) and wind flow (
). All vectors are measured in miles per hour. That is:
(1)
Let suppose that both north and east semiaxes are positive.
If we know that
and
, then the resultant velocity of the plane is:
![\vec v_{P} = \vec v_{E} + \vec v_{W}](https://tex.z-dn.net/?f=%5Cvec%20v_%7BP%7D%20%3D%20%5Cvec%20v_%7BE%7D%20%2B%20%5Cvec%20v_%7BW%7D)
![\vec v_{P} = (0\,mph, 300\,mph) + (-40\,mph\cdot \sin 20^{\circ},-40\,mph\cdot \cos 20^{\circ})](https://tex.z-dn.net/?f=%5Cvec%20v_%7BP%7D%20%3D%20%280%5C%2Cmph%2C%20300%5C%2Cmph%29%20%2B%20%28-40%5C%2Cmph%5Ccdot%20%5Csin%2020%5E%7B%5Ccirc%7D%2C-40%5C%2Cmph%5Ccdot%20%5Ccos%2020%5E%7B%5Ccirc%7D%29)
![\vec v_{P} = (0\,mph - 40\,mph\cdot \sin 20^{\circ}, 300\,mph -40\,mph\cdot \cos 20^{\circ})](https://tex.z-dn.net/?f=%5Cvec%20v_%7BP%7D%20%3D%20%280%5C%2Cmph%20-%2040%5C%2Cmph%5Ccdot%20%5Csin%2020%5E%7B%5Ccirc%7D%2C%20300%5C%2Cmph%20-40%5C%2Cmph%5Ccdot%20%5Ccos%2020%5E%7B%5Ccirc%7D%29)
![\vec v_{P} = (-13.681\,mph, 262.412\,mph)](https://tex.z-dn.net/?f=%5Cvec%20v_%7BP%7D%20%3D%20%28-13.681%5C%2Cmph%2C%20262.412%5C%2Cmph%29)
The resultant speed of the plane is determined by Pythagorean Theorem:
![\|\vec v_{P}\| = \sqrt{\left(-13.681\,mph\right)^{2}+\left(262.412\,mph \right)^{2}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v_%7BP%7D%5C%7C%20%3D%20%5Csqrt%7B%5Cleft%28-13.681%5C%2Cmph%5Cright%29%5E%7B2%7D%2B%5Cleft%28262.412%5C%2Cmph%20%5Cright%29%5E%7B2%7D%7D)
The plane travels at a speed of approximately 262.768 miles per hour.
Answer:
There is no common difference
Step-by-step explanation: