# Pre-Calc

An airplane’s velocity with respect to the air is 630 mph, and its heading is 𝑁 30° 𝐸. The wind, at the altitude of the plane, is directly from the southeast at 45° and has a velocity of 45 mph. Draw a figure that gives a visual representation of the situation. What is the true direction of the plane, and what is its speed with respect to the ground?

1. 👍
2. 👎
3. 👁
1. just convert the vectors to x-y components, add them, and you have the resultant.

Can you get that far? If not, where do you get stuck?

1. 👍
2. 👎
2. I did get to that part, I drew the picture, but I think I kept using the wrong angles, I'm not really sure

1. 👍
2. 👎
3. 630 @ 𝑁 30° 𝐸 = <315.00,545.58>
wind from the SE is in the direction NW, so 45 @ NW = <-31.82,31.82>

Now, if the plane's ground speed is <x,y> we have

<x,y> + <-31.82,31.82> = <315.00,545.58>

x = 346.82
y = 513.76

That translates into a speed of 619.87 in the direction (from the x-axis) of 55.98°. That makes a heading of 145.98°

1. 👍
2. 👎
4. sorry; the heading is 34.02°

(It's 90-A), not 90+A

1. 👍
2. 👎

## Similar Questions

1. ### phys

A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6 mph (with respect to the boat). The speed

2. ### Math

An airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the plane, is from the southwest and has a velocity of 60 miles per hour. What is the true

3. ### trig

An aifplane is flying on a compass heading (bearing) of 170* at 460 mph. A wind is blowing with the bearing 200* at 80mph. a) Find the component form of the velocity of the airplane. b) Find the actual ground speed and direction

4. ### Calculus

The power P (in W) generated by a particular windmill is given by P = .015 V^3 where V is the velocity of the wind (in mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.7 mph. P =

1. ### Trig

An airplane is flying on a compass heading (bearing) of 340 degrees at 325 mph. A wind is blowing with the bearing 320 degrees at 40 mph. Find the component form of the velocity of the airplane. then find the actual ground speed

2. ### Physics

An airplane is heading due east. The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air. If the wind is blowing from the north at 92.5 km/h, the velocity of the airplane relative to the

3. ### Pre-Cal

Two airplanes take off from an airport at the same time. One travels on a heading of 45 at 420 mph and the other on a heading of 150 at 400 mph. After two hours, how far apart are the airplanes? A.650.66 miles B.1,160 miles

4. ### word problem

An airplane is flying with a heading of 60 degrees east of north at 450 mph. A wind is blowing at 37 mph from the north. Find the plane's ground speed to the nearest mph and direction to the nearest degree. Thanks.

1. ### Trig/Precal

An airplane flies on a compass heading of 90° at 310 mph. The wind affecting the plane is blowing from 332° at 40 mph. What is the true course and ground speed of the airplane?

2. ### Physics

Two airplanes leave an airport at the same time. The velocity of the first airplane is 730 m/h at a heading of 44.6 degrees. The velocity of the second is 610 m/h at a heading of 100 degrees. How far apart are they after 2.3 h?

3. ### calculus

An airplane's velocity with respect to the air is 580 miles per hour, and its bearing is 332 degrees. The wind, at the altitude of the plane, is from the SW and has a velocity of 60 mph. What is the true direction of the plane,

4. ### physics

You are traveling on an airplane. The velocity of the plane with respect to the air is 180 m/s due east. The velocity of the air with respect to the ground is 40 m/s at an angle of 30° west of due north. 1)What is the speed of