# Vectors help with a airplane?

You are flying from Ottawa airport to Toronto airport a distance of 430km. The heading from Ottawa to Toronto is 225 degrees. You encounter a headwind blowing from a compass position of 190 degree of 50km/h your aircraft has a cruising speed of 200km/h what heading should u fly to reach Toronto what is your ground speed and how long will your flight take

### 1 Answer

- 6 years agoBest Answer
The Law of Sines can help determine course and airspeed. The desires flight path has a 35 degree variance from the headwind pushing it north, so the angle between the wind and path is 145 degrees. The gross path has a magnitude of 200 and the wind has a magnitude of 50; the angle between the gross path and the flight path is opposite the wind "side". Using the Law, the angle opposite the wind is sinA = 50 sin 145 / 200 = .25 sin 145 = 8.25 degrees; since he must fly further south, that means he must fly a heading of 217.

Now, what's his ground speed? Convert the compass headings to trig angles and add the vectors, so 200 km/hr at 217 resolves to 200 (cos 233 i + sin 233 j) and 50 km/hr at 10 (FROM 190, remember) = 50(cos 80 i + sin 80 j) = i(200 cos 233 + 50 cos 80) + j(200 sin 233 + 50 sin 80) = -111 i - 111 j = about 157 km/hr. (These results are rounded; you can get results as accurate as you want using a calculator.) A 430 km trip should then take 430/157 = 2.739 hr, about 2h45m.

Source(s): I'm a math teacher (not a pilot) in California.