a plane flies due north at 225km/h. a wind blows it due east at 55km/h. what is the magnitude and direction of the plane's resultant velocity?
measuring angles clockwise from N,
what is arctan 55/225 ?
magnitude: what is sqrt (225^2+55^2)
The magnitude is after that and then the degree is tan inverse y/x
To find the magnitude and direction of the plane's resultant velocity, you can use vector addition.
Step 1: Assign directions and magnitudes to the velocities:
- The plane's velocity due north is 225 km/h.
- The wind's velocity due east is 55 km/h.
Step 2: Draw a diagram:
Draw two vectors to scale, one pointing due north and the other pointing due east. The length of the vector representing the plane's velocity due north is 225 units (representing 225 km/h) and the length of the vector representing the wind's velocity due east is 55 units (representing 55 km/h).
Step 3: Add the vectors:
Place the tail of the vector representing the wind's velocity at the head of the vector representing the plane's velocity. Draw the resultant vector from the tail of the first vector to the head of the second vector.
Step 4: Measure the magnitude and direction of the resultant velocity:
Use a ruler to measure the length of the resultant vector on your diagram. Then convert this length to the appropriate scale (e.g., 1 unit = 10 km/h). This will give you the magnitude of the resultant velocity.
To find the direction, measure the angle between the resultant vector and the original north direction. You can use a protractor or a ruler to measure this angle. Clockwise angles are usually measured as negative, while counterclockwise angles are positive.
Step 5: Calculate the magnitude and direction:
Once you have the measurements, use the appropriate formulas to calculate the magnitude and direction of the resultant velocity. Typically, you can use the Pythagorean theorem to find the magnitude and trigonometry (e.g., sine and cosine functions) to find the direction.
In this case, the magnitude of the resultant velocity can be found by:
Magnitude = √(225^2 + 55^2)
The direction can be found using:
Direction = tan^⁻1(55/225)
By following these steps and performing the calculations, you can determine the magnitude and direction of the plane's resultant velocity.