Question

A plane is flying through the air at 120 kph toward the north while a wind is blowing toward the east with a speed of 50 kph. What is the magnitude of the actual velocity of the plane with respect to the ground?

Answer 1

The magnitude of the actual velocity of the plane with respect to the ground is 130 kph.

Step-by-step explanation:

To find the magnitude of the actual velocity of the plane with respect to the ground, we need to use vector addition. The velocity of the plane with respect to the ground can be found by adding the velocity of the plane in still air and the velocity of the wind.

In this case, the velocity of the plane in still air is 120 kph towards the north, and the velocity of the wind is 50 kph towards the east.

Using vector addition, we can calculate the magnitude of the resultant velocity:

Resultant velocity =
`\1\sqrt{120^(2) +50^(2)` =
`√(14400+2500)`=
`√(16900)` = 130 kph

Therefore, the magnitude of the actual velocity of the plane with respect to the ground is 130 kph.