Two planes take off from OR Tambo Airport shortly after each other. The one flies to Durban and the other flies to Cape Town. The one flying to Durban maintains an average speed of 700 km/h for the 550-km route, while the Cape Town flight maintains 750 km/h for its 1 450-km flight. The direction from OR Tambo to Durban is 57° south of east, while the direction from OR Tambo to Cape Town is 43º south of west.

Question

determine the velocity of the Cape Town flight relative to the Durban flight.

Answer 1

To determine the velocity of the Cape Town flight relative to the Durban flight, we need to find the vector sum of their velocities.

First, let's break down the velocities of each flight into their north-south and east-west components:

For the Durban flight:
North: 700 km/h * sin(57°) = 573.14 km/h
East: 700 km/h * cos(57°) = 409.71 km/h

For the Cape Town flight:
North: -750 km/h * sin(43°) = -514.85 km/h (negative because it is south)
West: -750 km/h * cos(43°) = -551.65 km/h (negative because it is west)

Now, let's find the vector sum of the velocities by adding the north and west components together:

Velocity of Cape Town flight relative to Durban flight:
North: -514.85 km/h - 573.14 km/h = -1088.99 km/h (negative because it is south)
West: -551.65 km/h - 409.71 km/h = -961.36 km/h (negative because it is west)

Therefore, the velocity of the Cape Town flight relative to the Durban flight is approximately 1089 km/h south and 961 km/h west.