Question

A pilot wants to fly west. If the plane has an airspeed of 95 m/s and there is a 25 m/s wind blowing north:
A. In what direction must she head the plane?
B. What will be her speed relative to the ground?
C. How far will the plane go in 2.25 h?

Can you explain how I would do this?

Answer 1

Head T degrees south of west
then
95 sin T = 25
sin T = .263
T = 15.25 degrees south of west
now
total speed north over ground = 0
Vw = total speed west over ground = 95 cos 15.25 m/s
so in 2.25 hr distance = 2.25 * Vw

Answer 2

All angles are measured CW from +y-axis.

A. Vr = Vp + 25i = 95m/s[270o] = Resultant velocity,

Vp + 25i = 95*sin270 + (95*Cos270)I,

Vp + 25i = -95 + 0i,

Vp = -95 - 25i = 98m/s[75o] W. of S. = 255o CW.

Direction = 75o W. of S. = 15o S. of W. = 255o CW.

B. Speed = 98 m/s(Part A.).

C. d = Vr * T = 95 * 2.25 = ___m.