A flight controller determines that an airplane is 34.0mi south of him. Half an hour later, the same plane is 42.0mi northwest of him.
The general direction of the airplane’s velocity is?
If the plane is flying with constant velocity, what is the direction of its velocity during this time, degrees north of west?
What is the magnitude of its velocity during this time?
d = 42m1[135o] - 34mi[270o]
X = 42*Cos135 = -29.7 mi
Y = 42*sin135 - 34*sin270 = 63.7 mi.
Tan A = Y/X = 63.7/-29.7 = -2.14473
A = -65o = 65o N. of W. = 115o, CCW.
d = Y/sin A = 63.7/sin 115 = 70.3 mi.
d = V*t = 70.3
V = 70.3/t = 70.3/0.5h = 140.6 mi/h
To find the general direction of the airplane's velocity, we can draw a diagram and use basic trigonometry.
Step 1: Draw a diagram representing the flight controller's position and the initial position of the airplane, which is 34.0 miles south of him.
Step 2: Draw a line from the initial position of the airplane to its final position, which is 42.0 miles northwest of the flight controller.
Step 3: Connect the initial position, flight controller's position, and final position to form a triangle.
Step 4: Determine the angle between the line connecting the initial and final positions of the airplane and the line connecting the flight controller's position and the final position.
Step 5: The general direction of the airplane's velocity is the direction of the line connecting the initial and final positions.
To find the direction of the airplane's velocity in degrees north of west:
Step 1: Use the triangle formed in the previous steps.
Step 2: Determine the angle between the line connecting the flight controller's position and the final position and the westward direction.
Step 3: Calculate the direction of the airplane's velocity in degrees north of west.
To find the magnitude of the airplane's velocity during this time:
Step 1: Use the triangle formed in the first steps.
Step 2: Calculate the distance between the initial and final positions of the airplane.
Step 3: Divide the distance by the time (which is half an hour) to find the magnitude of the velocity.
Let me know if you need further assistance with any of these steps!
To determine the general direction of the airplane's velocity, we can use the information given that the airplane is initially 34.0 miles south of the flight controller and then 42.0 miles northwest of him half an hour later.
To find the general direction, we can draw a vector diagram.
1. Start by drawing a coordinate system with the flight controller at the origin (0,0).
2. Place the initial position of the airplane 34.0 miles south of the flight controller.
3. Next, draw a line from the initial position of the airplane to its final position, which is 42.0 miles northwest of the flight controller.
4. The direction of the line from the initial to the final position represents the general direction of the airplane's velocity.
5. Finally, you can use a compass or other tools to determine the angle between the line and the west direction in degrees.
To find the magnitude of the airplane's velocity during this time, we can calculate the displacement using the Pythagorean theorem.
1. Since the airplane flies half an hour, we can consider this as the time interval.
2. Use the Pythagorean theorem to find the displacement of the airplane, which is the straight-line distance between its initial and final positions:
displacement^2 = (34.0 mi)^2 + (42.0 mi)^2
3. Take the square root of the calculated displacement to find the magnitude of the velocity.
Thus, by following these steps, you can determine the general direction of the airplane's velocity and the magnitude of its velocity during this time.