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Finding Your Way Home A GPS receiver indicates that your home is 150 km and 400 north of west, but the only path through the woods leads directly north If you follow the path 50 km before it opens into a field, how far, and in what direction, would you have to walk to reach your home

Set the width of your window to 480 pixels, and the height to 130 pixels. Set the x value of the window to 100, which indicates that we want the window s initial position to be on the left side of the screen. The y value can be a little more problematic. The coordinate system on your Mac s screen has 0 at the lower-left corner of the screen, with the y value getting higher as you move up toward the top of the screen. The problem here is that not everybody has the same size monitor, so any given y value will be different relative to the top of the screen on different size monitors.

Draw the resultant vector, R, from your original location to your home Draw A, the known vector, and draw B, the unknown vector Known:

Unknown:

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Find the components of R Rx R cos (150 km) cos 1400 115 km Ry R sin (150 km) sin 1400 964 km Because A is due north, Ax

1800 400

1400

150 km,

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1400

150 km,

1400

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Use the components of R and A to find the components of B Bx Rx Ax 115 km 00 km Substitute Rx 115 km, Ax 00 km 115 km The negative sign means that this component points west By Ry Ay 964 km 50 km Substitute Ry 964 km, Ay 50 km 46 km This component points north Use the components of vector B to find the magnitude of vector B B Bx2 12 km Use the tangent to find the direction of vector B tan tan

By2 (46 km)2

Fortunately, Cocoa will automatically adjust the window s position so that the window always starts on the screen, even if the location you specify would otherwise place it offscreen somewhere, and because we gave the window an autosave name, every time the user launches the application after the first, the window will be where it was when he last quit the application But, sometimes it s important that a window start in a particular position relative to the top of the screen Do you see the little diagram at the bottom of the size inspector It gives you a visual representation of the window s initial position based on your own screen s size The little white box represents the window, and the big box represents the screen minus the menu bar.

( 115 km)2

Locate the tail of vector B at the origin of a coordinate system and draw the components Bx and By The direction is in the third quadrant, at 158 , or 22 north of west Thus, B 12 km at 22 north of west

Are the units correct Kilometers and degrees are correct Do the signs make sense They agree with the diagram Is the magnitude realistic The length of B should be longer than Rx because the angle between A and B is greater than 90

Solve problems 5 10 algebraically You may also choose to solve some of them graphically to check your answers

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