vectors and velocity

Question

an airplane is taking off headed due north with an air speed of 173mph at an angle of 18\deg relative to the horizontal. the wind is blowing with a velocity of 42 miles per hour at an able of S^(47)\deg E. find a vector that represents the resultant velocity of the plane relative to the point of takeoff. let i point east, j point north and k point up. show work

Answer 1

Hello Cin G.

3 Dimensional Vector notation comes in two forms, Polar and Rectangular.

Polar from equals a magnitude and two angles, one for the x-y plane, and one for the z plane.

Example: Polar = |mag| ang theta , ang Phi . In rectangular this would result in a x-y-z vector of three numbers which represent motion or forces in the i-j-k.

The aircraft is flying North (x-y angle 90) and 18 degrees nose up - meaning +18 on the k axis, so the vector of the aircraft is: 173 mph ang 90 ang 18, or 0i +53.3j+164.5k.

The wind is blowing at 43 mph 47 degrees south of east. This is a horizontal only velocity with no vertical component. So the vector of the wind is in polar = 43 mph ang 313 ang 0, or 29.3i-31.4j+0k

To solve the problem you add all the 'i''s together, and do the same for the 'j' and 'k components.

The resultant is 29.3i+22.1j+164.5k in rectangular, and in polar equals an magnitude of 168.6 mph ang 37 ang 12.6. Please consult me if you desire a diagram of this problem. I created a diagram using the whiteboard system. My tutor name is 'Huey S'.