Question

A train is travelling in a westerly direction at 100 km/h. A passenger notices an aeroplane appearing to fly at 180 km/h south. Using a velocity diagram, calculate the actual velocity and direction of the aeroplane.

Answer 1

To calculate the actual velocity and direction of the airplane, we can use vector addition.

Let the velocity of the train be vector T, pointing to the west with magnitude 100 km/h.
Let the velocity of the airplane be vector A, pointing to the south with magnitude 180 km/h.

We want to find the resultant velocity R of the airplane, which is the sum of vectors T and A. To do this, we can draw a velocity diagram.

1. Draw vector T (100 km/h) pointing to the left (west).
2. Draw vector A (180 km/h) pointing down (south).
3. Draw vector R as the sum of vectors T and A, connecting the tail of T to the head of A.

To find the magnitude and direction of vector R, we can use the Pythagorean theorem and trigonometry.

Magnitude of R = sqrt((100)^2 + (180)^2) = sqrt(10000 + 32400) = sqrt(42400) ≈ 206 km/h

To find the direction of vector R, we can use the tangent function:

tan(theta) = opposite/adjacent
tan(theta) = 180/100
theta = arctan(180/100) ≈ 60.9 degrees

Therefore, the actual velocity and direction of the airplane is approximately 206 km/h in a southwesterly direction.