A plane has a velocity of 400 mph to the SW. A wind from the west is blowing at 50 mph. Find the resultant speed and direction.



How do i find resultant speed without a direction.

SW is a direction.

Make a sketch on the N-S-E-W grid
SW is in the third quadrant, dividing it into two parts of 45° each.
Draw such a line OP, marking its length as 400 mph, and O at the origin. Draw a line PR horizontally to the right and mark it 50.

So now you have a triangle POR, where OP=400, angle OPR = 45 and PR = 50
By the cosines law:
OR^2 = 400^2 + 50^2 - 2(400)(50)cos45°
= ..
OR = √ ....
Now by the Sine law:
sinR/400 = sin45/OR
We can find angle R, then the direction of OR

Well, it seems you're looking for the resultant speed without a direction, but that's like trying to follow a map without knowing where you're going! Direction is a crucial element in determining the resultant speed. However, if you're only interested in the numerical value without direction, you can use vector addition to find the magnitude of the resultant velocity. In this case, you would use the Pythagorean theorem to calculate the square root of the sum of the squares of the velocities in the x and y directions. So, in mathematical terms, the resultant speed would be:

√(400^2 + 50^2) mph

Now, I hope you have a clear sense of how to find that direction, because we wouldn't want you to wander off into the wrong direction like a confused clown at a circus!

To find the resultant speed without a direction, you can use vector addition. Here's how you can calculate it:

1. Draw a vector diagram to represent the given velocity of the plane and the wind vector.
2. The velocity of the plane is given as 400 mph to the southwest. To represent this vector on the diagram, draw an arrow pointing in the southwest direction with a length proportional to the magnitude of 400 mph.
3. The wind vector is given as blowing from the west at 50 mph. To represent this vector on the diagram, draw an arrow pointing due west with a length proportional to the magnitude of 50 mph.
4. Now, add these two vectors by placing the tail of the wind vector at the head of the plane velocity vector. Draw a new arrow from the tail of the plane velocity vector to the head of the wind vector.
5. The resultant vector represents the combined effect of the plane's velocity and the wind. Measure the length of the resultant vector.
6. The length of the resultant vector is the resultant speed.

By following these steps, you can find the resultant speed without considering the direction.

To find the resultant speed without a direction, you can simply add the magnitudes of the velocities involved.

Here, the plane's velocity is given as 400 mph to the southwest. Since velocity is a vector quantity, it has both magnitude (speed) and direction. However, for finding the resultant speed only, we can ignore the direction for now.

The wind is blowing from the west at 50 mph. Note that "from the west" means the wind is blowing in the opposite direction of the west, which is towards the east.

To find the resultant speed, add the magnitudes (speeds) of the plane's velocity and the wind's velocity:

Resultant speed = Magnitude of plane's velocity + Magnitude of wind's velocity
= 400 mph + 50 mph
= 450 mph

Therefore, the resultant speed is 450 mph.