Question

A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 243 km and a direction 30.0o north of east. The displacement vector for the second segment has a magnitude of 178 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle ? with the direction due east. Using the component method, find (a) the magnitude of R and (b) the directional angle ?.

(a) R = km
(b) ? = degrees

Answer 1

a)
`R=126Km`

b)
`\theta=74.6\textdegree`

Step-by-step explanation:

From the question we are told that:

1st segment

243km at Angle=30

2nd segment

178km West

Resolving to the X axis

`F_x=243cos30+178`

`F_x=33.44Km`

Resolving to the Y axis

`F_y=243sin30+178sin0`

`R=√(F_y^2+F_x^2)`

`F_y=121.5Km`

Therefore

Generally the equation for Directional Angle is mathematically given by

`\theta=tan^(-1)(F_y)/(F_x)`

`\theta=tan^(-1)(121.5)/(33.44)`

`\theta=74.6\textdegree`

Generally the equation for Magnitude is mathematically given by

`R=√(F_y^2+F_x^2)`

`R=√(33.44^2+121.5^2)`

`R=126Km`