Question
The pilot of an aircraft wishes to fly due
west in a 52.6 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 154 km/h.
A.) How many degrees from west should the aircraft head? Let clockwise be positive. Answer in units of ◦ (degrees)
B.) What should the plane’s speed be relative to the ground? Answer in units of km/h.
west in a 52.6 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 154 km/h.
A.) How many degrees from west should the aircraft head? Let clockwise be positive. Answer in units of ◦ (degrees)
B.) What should the plane’s speed be relative to the ground? Answer in units of km/h.
Answers
X = -154 km/h.
Y = -52.6 km/h = Speed of wind.
A. tanAr = Y/X = -52.6/-154 = 0.34156.
Ar = 19o = Reference angle.
A = Ar + 180 = 19 + 180 = 199o. = 19o
South of West.
The plane should head 19o North of West.
B. V^2 = X^2 + Y^2.
V^2 = (-154)^2 + (-52.6)^2 = 26482.76
V = 163 km/h.
Y = -52.6 km/h = Speed of wind.
A. tanAr = Y/X = -52.6/-154 = 0.34156.
Ar = 19o = Reference angle.
A = Ar + 180 = 19 + 180 = 199o. = 19o
South of West.
The plane should head 19o North of West.
B. V^2 = X^2 + Y^2.
V^2 = (-154)^2 + (-52.6)^2 = 26482.76
V = 163 km/h.