A plane takes off from a city and heads east 1100 km away. The plane is flying d

Question

A plane takes off from a city and heads east 1100 km away. The plane is flying due east at a speed of u=Ae^Bt where A = 30ms^-1 and B = 5•10^-4 s^-1. assume a latitude of 42.5 degrees North.
a) The plane has an initial N-S velocity of 0. Write an equation for the v-component of the wind as a function of time assuming the only force upon the plane is the Coriolis force.
b) Due to the Coriolis Force, the plane will not be able to fly due east as the coriolis force will create a N-S velocity. How far to the North or South will the plane be after 1 hour of flight? A plane takes off from a city and heads east 1100 km away. The plane is flying due east at a speed of u=Ae^Bt where A = 30ms^-1 and B = 5•10^-4 s^-1. assume a latitude of 42.5 degrees North.
a) The plane has an initial N-S velocity of 0. Write an equation for the v-component of the wind as a function of time assuming the only force upon the plane is the Coriolis force.
b) Due to the Coriolis Force, the plane will not be able to fly due east as the coriolis force will create a N-S velocity. How far to the North or South will the plane be after 1 hour of flight? A plane takes off from a city and heads east 1100 km away. The plane is flying due east at a speed of u=Ae^Bt where A = 30ms^-1 and B = 5•10^-4 s^-1. assume a latitude of 42.5 degrees North.
a) The plane has an initial N-S velocity of 0. Write an equation for the v-component of the wind as a function of time assuming the only force upon the plane is the Coriolis force.
b) Due to the Coriolis Force, the plane will not be able to fly due east as the coriolis force will create a N-S velocity. How far to the North or South will the plane be after 1 hour of flight?

Explanation / Answer

(a) The air speed should nullify the speed of the airplane in the west direction since wind is blowing part east and part north.

Wind speed part east : 40/21/2

(angle is 45 degrees so cos 45 = 1/21/2)

So speed of plane in west direction = ground speed - speed of wind in east direction = 350 - 40/21/2 = u

Speed of plane in north direction = speed imparted by wind blowing in part north direction = 40/21/2 = v

Total speed = [u2+v2]1/2

Therefore v = (310 km/hr) (cos theta)x + (310 km/hr) (sin theta) y + (75 km/hr)x

=cos theta = -75 / 310 = -15 /62 1040 = 140west of north.

(b) To find out how far to the North or South will the plane be after 1 hour of flight, let us use the following equation:

Theta = tan-1 (0.60m / 20m) = 1.7 0.

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