Posted by **Becky** on Friday, August 31, 2012 at 3:09pm.

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 200 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. (Round your answers to one decimal place.)

- calc 3 -
**MathMate**, Friday, August 31, 2012 at 3:19pm
Trouble-free way to get resultant:

resolve into x- and y-components and add.

Wind is FROM N45W, which means that its direction is S45E.

Take East = x, and North = y,

the wind vector is then

<40sin(45),40cos(45)>

The velocity vector of the plane is

<200sin(60),200cos(60)>

The combined vector (resultant) is therefore

<40sin(45)+200sin(60), 40cos(45)+200cos(60)>

Find the magnitude and direction of the resultant in the usual way.

## Answer this Question

## Related Questions

- math - An airplane travels with a speed of 145 mph in calm air. the wind is ...
- Physics - HELP - An airplane is heading due south at a speed of 515 km/h. A wind...
- physics - An airplane is heading due south at a speed of 515 km/h. A wind begins...
- Math - Me, again... Please help me. Thank you. Assume a plane is flying directly...
- physics - An aircraft is flying at the speed of 354km/hr relative to the air is ...
- MATH - AN AIRPLANE HEADS DUE NORTH 100MPH. IT EXPERIENCES A 20 MPH WIND FLOW IN ...
- science - Paul threw a paper plane towards the west. The wind however caused the...
- Physics - An aircraft has a cruising speed of 100 m/s On a particular day, a ...
- physics - An aircraft in straight and level flight is in a state of horizontal ...
- Geometry - A plane is is flying 225 mph heading S25°W. The wind is blowing S80°E...

More Related Questions