A novice pilot sets a plane's controls, thinking the plane will fly at 2.50 * 10*2 km/h to the north. If the wind blows at 75 km/h toward the southeast, what is the plane's resultant velocity? Use graphical techniques

please show me how to solve this.
the answer i need to come to is 204 km/h at 75degrees North of East

To solve this problem using graphical techniques, we can use vector addition. We will break down the motion of the plane and wind into their respective components and then add them together to find the resultant velocity.

Step 1: Set up the coordinate system
Draw a coordinate system with an x-axis pointing east and a y-axis pointing north. Label the direction of the wind as southeast, which means it is blowing towards the southeast, making an angle of 45 degrees with the negative x-axis.

Step 2: Break down the wind velocity
The wind is blowing at 75 km/h towards the southeast. We can find its x and y components using trigonometry. Since the angle between the wind and the positive x-axis is 45 degrees, the x-component is given by:

Wind_x = Wind_speed * cos(angle)
= 75 km/h * cos(45)
= 75 km/h * 0.707
≈ 53.03 km/h

Similarly, the y-component is given by:

Wind_y = Wind_speed * sin(angle)
= 75 km/h * sin(45)
= 75 km/h * 0.707
≈ 53.03 km/h

So, the wind has an x-component of 53.03 km/h towards the east and a y-component of 53.03 km/h towards the south.

Step 3: Draw the wind vector
Starting from the origin of the coordinate system, draw an arrow representing the wind velocity. From the origin, draw an arrow pointing 53.03 km/h towards the east and 53.03 km/h towards the south. Label this vector as the wind vector.

Step 4: Break down the plane's velocity
The plane is supposed to fly at a velocity of 2.50 * 10^2 km/h to the north. We can break down its velocity into x and y components. Since it is moving straight north, its x-component will be zero, and the y-component will be:

Plane_y = Plane_speed * sin(angle)
= 2.50 * 10^2 km/h * sin(90)
= 2.50 * 10^2 km/h * 1
= 2.50 * 10^2 km/h

So, the plane has an x-component of 0 km/h and a y-component of 2.50 * 10^2 km/h towards the north.

Step 5: Draw the plane's velocity vector
Starting from the origin, draw an arrow representing the plane's velocity. Since the plane is moving straight north, draw an arrow pointing 2.50 * 10^2 km/h straight up. Label this vector as the plane's velocity vector.

Step 6: Add the vectors
To find the resultant velocity, add the wind vector and the plane's velocity vector. Place the tail of the plane's velocity vector at the head of the wind vector.

Step 7: Measure the resultant velocity
Measure the magnitude of the resultant velocity vector using a ruler. Measure the angle it makes with the positive x-axis using a protractor or angle-measuring tool.

The magnitude of the resultant velocity is approximately 204 km/h, and the angle it makes with the positive x-axis (east) is approximately 75 degrees. Therefore, the plane's resultant velocity is 204 km/h at 75 degrees north of east.

To solve this problem using graphical techniques, we will be using vector addition. Vector addition involves the geometric representation of vectors as arrows, where the length of the arrow represents the magnitude (speed) of the vector and the direction of the arrow represents the direction of the vector.

Here's how you can solve the problem step by step:

1. Draw a reference coordinate system with an x-axis (horizontal) and a y-axis (vertical). Let's assume the positive x-axis points towards the east and the positive y-axis points towards the north.

2. Draw an arrow representing the plane's intended velocity of 2.50 * 10^2 km/h pointed directly north. Since there is no wind, this velocity vector will point directly up along the y-axis. Make the length of this arrow proportional to the magnitude (2.50 * 10^2 km/h).

3. Draw another arrow representing the wind velocity of 75 km/h towards the southeast. Since the wind blows towards the southeast, the arrow should point in that direction. Use a protractor or estimate the approximate direction. Make the length of this arrow proportional to the magnitude (75 km/h).

4. Now, using the head-to-tail method of vector addition, position the tail of the wind velocity arrow at the head of the plane's intended velocity arrow. Think of this as connecting the two arrows.

5. Draw a new arrow starting from the tail of the plane's intended velocity and ending at the head of the wind velocity. This new arrow represents the resultant velocity of the plane.

6. Measure the length of the resultant arrow using a ruler. This length represents the magnitude of the resultant velocity.

7. Measure the angle between the positive x-axis (east) and the direction of the resultant velocity arrow using a protractor. This angle represents the direction of the resultant velocity.

8. Convert the length of the resultant velocity arrow to the appropriate units if needed (e.g., from km/h to m/s).

Based on your expected answer, you should find that the magnitude of the resultant velocity is 204 km/h and the direction is 75 degrees north of east.

googly eyes

Viva