Question

A plane can fly 85 m/s in still air. The pilot wants to fly to a destination due east of his starting point. There is a wind blowing 20 m/s north. What direction should the pulley direct the plane?

Answer 1

Step-by-step explanation:

if we just go East, the plane will actually fly along a line with the slope 20/85 = 4/17, as for every 85 meters the plane flies East, it also goes 20 meters North.

therefore, in order to go actually East, the plane has to fly along a line, where it goes South 20 m/s while going East 85 m/s.

this line has a slope of -20/85 = -4/17.

in any case, this creates a right-angled triangle with the legs of 85 m and 20 m.

and we are looking at the angle alpha at the origin as the direction of the flight.

20 = tan(alpha) × 85

tan(alpha) = 20/85 = 4/17 = 0.235294118...

alpha = 13.24051992...°

the plane has to aim for East 13.24051992...° South (about East-South-East) to go truly East.

Answer 2

the pulley should direct the plane at an angle of 13.3° north of due east.

Step-by-step explanation:

To determine the direction the pilot should direct the plane, we need to consider the combined effect of the plane's velocity and the wind velocity.

The plane's velocity in still air is 85 m/s due east. The wind is blowing with a velocity of 20 m/s north.

We can break down the plane's velocity into its horizontal and vertical components using trigonometry. The horizontal component represents the plane's velocity in the east direction, and the vertical component represents the plane's velocity in the north direction.

The horizontal component of the plane's velocity is given by 85 m/s * cos(0°), which is equal to 85 m/s.

The vertical component of the plane's velocity is given by 85 m/s * sin(0°), which is equal to 0 m/s.

The wind's velocity is entirely in the north direction, with no eastward component.

To find the resultant velocity, we add the horizontal components and vertical components separately.

The resultant horizontal component is the sum of the plane's horizontal velocity and the wind's horizontal velocity, which is 85 m/s + 0 m/s = 85 m/s.

The resultant vertical component is the sum of the plane's vertical velocity and the wind's vertical velocity, which is 0 m/s + 20 m/s = 20 m/s.

Using trigonometry, we can find the direction of the resultant velocity. The angle θ can be calculated as the arctan(vertical component / horizontal component).

θ = arctan(20 m/s / 85 m/s) = 13.3°

Therefore, the pulley should direct the plane at an angle of 13.3° north of due east.