I thought I\'d post again to see if my mathematical equations hold when I ask th
ID: 2166439 • Letter: I
Question
I thought I'd post again to see if my mathematical equations hold when I ask the question
Find the direction and magnitude of the following vectors.
Part A 30 -8.0
Express your answer as a whole number. =
counterclockwise from the positive axis Part B Express your answer using two significant figures. =
Part C 4.0 20 Express your answer as a whole number. =
counterclockwise from the positive axis Part D Express your answer using two significant figures. =
Part E =
counterclockwise from the positive axis
Part F Express your answer using two significant figures. =
Explanation / Answer
Any vector can be broken up into x and y components so that they can be added easily The x-component is normally considered to be positive when it points to the right and negative when it points to the left. The y-component is normally considered to be positive when it points vertically upwards and negative when it points vertically down. The x and y components are at right angles to each other. Draw a diagram with a horizontal line with an arrow to the left and mark it as 25.0 units. Now draw a vertical line from the arrow head (ie the left hand end in this case) of the first line, which goes upwards on the page and which is at right angles to the first line. Put an arrow at the top and mark it as 40.0 units. Now join the righthand end of the first line to the tip of the arrow of the second line. This is the resultant vector that you want the magnitude and direction of. You now have a right angled triangle to solve. To find the magnitude, just use Pythagoras to find the length of the hypotenuse. To find the direction use simple trigonometry on the triangle. Use the tan ratio to find the angle between the hypotenuse and the adjacent side ( ie the x-component). Then describe the direction in the best way that suits the question. For example, in this case the angle is tan^(-1) (40/25) = 58º to the nearest degree. So the direction could be described as in a direction of (180 - 58)º = 122º with the positive direction of the x-axis. Or maybe in a direction (90 - 58)º = 32º left of the vertical. How you describe it is not important as long as the direction is clear from your description, but the horizontal is most commonly used.