a small plane flies due south with a speed of 112 m/s while a tailwind blows due south at 31 m/s. Draw and label a vector diagram and calculate the magnitude and direction of the plane's resultant velocity

Cannot draw diagrams on these posts.

Since both the flight direction and the wind are due south, just add the two velocities to get

143 m/s

draw a straight line pointing south, and label its length as 142

btw, 112 m/s for a small plane
= 112(60)(60) or 403200 m/h
= 403 km/h or appr 250 mph, average speed of a small plane is about 150 mph


and a windspeed of 31 m/s is appr 87 km/h

result: a very fast small plane flying in a hurricane.

To draw a vector diagram, follow these steps:

1. Choose a scale for the diagram. For example, you could use 1 cm to represent 20 m/s.
2. Draw a horizontal line to represent the ground, and label it as the x-axis.
3. Draw a vertical line perpendicular to the x-axis, and label it as the y-axis.
4. Label the starting point of the plane's velocity vector as "O" (the origin).
5. Draw a vector from point O to the right along the x-axis, representing the plane's initial velocity of 112 m/s.
6. Label that vector as "Vp" (plane's velocity).
7. Draw a vector parallel to the x-axis starting from the tip of Vp and extending to the right, representing the tailwind's velocity of 31 m/s.
8. Label this vector as "Vtw" (tailwind's velocity).
9. Draw a dashed line connecting the tail of Vp to the tip of Vtw, representing the plane's resultant velocity.
10. Label this resultant vector as "Vr" (resultant velocity).

To calculate the magnitude and direction of the resultant velocity:

1. Break down the given velocities into their components along the x-axis.
- Plane's velocity (Vp) component along x-axis (Vpx) = 112 m/s
- Tailwind's velocity (Vtw) component along x-axis (Vtwx) = 31 m/s
- Since both velocities are in the same direction, their x-components simply add up.

2. Calculate the resultant velocity (Vr) along the x-axis.
- Vrx = Vpx + Vtwx
- Vrx = 112 m/s + 31 m/s
- Vrx = 143 m/s

3. The magnitude of the resultant velocity is the length of the dashed line representing Vr, which can be found using the Pythagorean theorem.
- Vr^2 = Vrx^2 + Vry^2
- Vry = 0 (since the plane flies due south)
- Vr^2 = Vrx^2
- Vr = sqrt(Vrx^2)
- Vr = sqrt((143 m/s)^2)
- Vr ≈ 143 m/s

4. The direction of the resultant velocity can be found using trigonometry. The plane is flying due south, so the angle between Vr and the negative x-axis is 180 degrees.
- Therefore, the direction of the resultant velocity is south.

Therefore, the magnitude of the plane's resultant velocity is approximately 143 m/s, and its direction is due south.