Physics question......confused?

Question

An ariplane is flying at 150 mi/h (its speed in still air) in a direction such that with wind of 60.0 mi/h blowing from east to west, the airplane travels in a straight line southward. (a) What must the plane's heading (direction) for it to fly directly south? (b) If the plane has to go 200 mi in the southward direction, how long does it take?

Answer 1

Draw a right triangle (vectors) with the hypotenuse 150 units long pointing slightly southeast, and the base 60 units long horizontally (east/west). The third side of the triangle, pointing straight down (south) is the plane's actual track over the ground.

The airplane's heading would be the angle between due north and the hypotenuse. The easiest way to do this is to determine the angle between the plane's heading and its track - using trig is probably easiest. The sine of the angle is equal to the wind speed divided by the plane's airspeed, or 60/150 = 0.4. The arcsin of 0.4 is 23.58°, so the plane's heading would be 180° minus 23.58° or about 156° (using the standard convention that North is 0° and East is 90°).

The plane's ground speed is the third side of the triangle. Using the Pythagorean theorem, the length of the third side is sqrt(150² - 60²) = 137.5 mi/hr. To travel 200 miles would take 200/137.5 = 1.45 hours, or about 1 hour 27 minutes.