Question

learning goal: to understand and be able to calculate the components of vectors. you have heard vectors defined as quantities with magnitude and direction, familiar ideas also found in statements such as \three miles northeast of here.\ components, the lengths in the x and y directions of the vector, are a different way to define vectors. in this problem, you will learn about components, by considering ways that they arise in everyday life. suppose that you needed to tell some friends how to get from point a to point b in a city. the net displacement vector from point a to point b is shown in the figure (figure 1). you could tell them that to get from a to b they should go 3.606 blocks in a direction 33.69° north of east. however, these instructions would be difficult to follow, considering the buildings in the way. part a you would more likely give your friends a number of blocks to go east and then a number of blocks to go north. what would these two numbers be? enter the number of blocks to go east, followed by the number of blocks to go north, separated by a comma. part b complete previous part(s) part c complete previous part(s) part d complete previous part(s) part e complete previous part(s) part f complete previous part(s)

Explanation:

Step1: Identify the vector - component formula

If the magnitude of the vector is $r = 3.606$ blocks and the angle with the east - direction $\theta=33.69^{\circ}$, the east - west (x - component) and north - south (y - component) of the vector can be found using trigonometry. The x - component (east - direction) is given by $x = r\cos\theta$ and the y - component (north - direction) is given by $y = r\sin\theta$.

Step2: Calculate the east - component

$x = 3.606\times\cos(33.69^{\circ})$. Since $\cos(33.69^{\circ})\approx0.832$, then $x = 3.606\times0.832\approx3$.

Step3: Calculate the north - component

$y = 3.606\times\sin(33.69^{\circ})$. Since $\sin(33.69^{\circ})\approx0.555$, then $y = 3.606\times0.555\approx2$.

Answer:

3,2