a boeing 747 jet maintains an airspeed of 650 miles per hours in a southwesterly direction. the velocity of the jet stream is a constant 80 miles per hour from the west. find the actual speed and direction of the aircraft.

how do i set this up? can anyone walk me through the steps, i can't figure it out. :[

654.7

To solve this problem, you can use vector addition. Here are the steps to set it up:

1. Draw a diagram: Draw a coordinate grid with North (N) pointing upwards, South (S) pointing downwards, East (E) pointing to the right, and West (W) pointing to the left. Draw an arrow representing the velocity of the jetstream pointing to the left (West). Label this arrow with a magnitude of 80 mph.

2. Define vectors: Let's define two vectors: V_jet representing the airspeed of the jet and V_jetstream representing the velocity of the jetstream.

3. Analyze vectors direction and magnitude: The given airspeed of the jet is 650 mph in a southwesterly direction. You can break it down into two components: a southern component and a western component. To find the magnitude of each component, you can use the Pythagorean theorem.

- Southern component: Use the given magnitude of 650 mph and the angle formed by the southwesterly direction to find the magnitude of the southern component (V_jet_south).
- Western component: Use the given magnitude of 650 mph and the angle formed by the southwesterly direction to find the magnitude of the western component (V_jet_west).

4. Determine vector addition:
Now, add the two vectors together: V_result = V_jet + V_jetstream.
To find the magnitude of the resultant vector (V_result), you can use the Pythagorean theorem once again.
To find the direction of the resultant vector, you can use the tangent inverse of the angle formed by the southwesterly direction.

5. Calculate actual speed and direction:
The actual speed of the aircraft is the magnitude of the resultant vector (V_result).
The direction of the aircraft is the angle formed by the southwesterly direction and can be stated as either a compass direction or an angle.

By following these steps, you should be able to find the actual speed and direction of the aircraft.