Question

An airplane travels at 125 km/hr...?

An airplane travels at 125 km/hr for 2 hours in a direction of 250°.

At the end of this time, how far south of the airport is the airplane? How many kilometers south?

Note: Directions are given in degrees clockwise from north

Thanks friends

Answer 1

We will need to use trigonometric functions to solve this problem. Trigonometric functions are referenced to the equivalent of East and the positive direction is counterclockwise. Therefore, we must convert the angle:

`theta = -250^@ + 90^@`

`theta = -160^@`

The radial distance vector, `r`. is:

`r = 125" km/hr" xx 2" hr"`

`r = 250" km"`

The polar vector `vecr =(r, theta)` is:

`vecr = (250" km", -160^@)`

The Cartesian form is:

`vecr = (250" km")cos(-160^@)hati+ (250" km")sin(-160^@)hatj`

`vecr = (250" km")cos(-160^@)hati+ (250" km")sin(-160^@)hatj`

`vecr = (-234.9" km")hati+ (-85.5" km")hatj`

The `hatj` vector component corresponds to North, therefore, the airplane is `85.5" km"` South of the airport.