Question

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 39m/s . The plane is in a 12m/s wind blowing toward the southwest relative to the earth.

Question A:

Letting x be east and y be north, find the components of v? P/E (the velocity of the plane relative to the earth).

Question B:

Find the magnitude of v? P/E.

Question C:

Find the direction of v? P/E.

Any help is appreciated!

Answer 1

Velocity of plane:

v = 39 m/s towards South

Velocity of air:

v' = 12 m/s towards south west

Let the coordinate axis be such that, north is +y, south is -y, west : -x and east +x.

Now velocity of plane:

v = -39 j m/s

or, in component form:

v_x = 0 m/s

v_y = -39 m/s

And velocity of air:

v' = 12 m/s south west (at an angle 45 deg relative to -x and -y axes)

So,

v' = -12 cos 45 i -12 sin 45 j m/s

In component form:

v'_x = -12 cos 45 m/s

v'_y = -12 sin 45 m/s

Now we find net veloocity of plane, or velocity of plane relative to earth: (It is the vector addition of two velocities: v and v'

V = v + v'

A.

In component form:

V_x = v_x + v'_x = 0 - 12 cos 45 = -8.484 m/s

And

V_y = v_y + v'_y = -39 -12 cos 45 = -39 -8.484 = -47.484 m/s

Thus total velocity V:

V = v + v' = -8.484 i - 47.484 j m/s

B.

Magnitute of V:

C.

Direction of V:

or,

Since the plane is flying south and wind is in south east this angle is relative to -x axis.

Thus direction of plane with respect to earth is 79.9 deg towards south-east.

Direction: 79.9 deg SOUTH - EAST.