1) The distance of the store from the house is 4.47 blocks
2) The horizontal component of the vector is 37.7 N, the vertical component is 16.0 N
3) The magnitude of the resultant vector is 11.6 m
Explanation:
1)
Jeremy's motion is divided into two parts:
- First, a motion of 4 blocks east
- Then, a motion of 2 blocks south
Here we want to measure the distance between the initial and final position of Jeremy.
We notice that the two displacements are perpendicular to each other, so they correspond to the sides of a right triangle, of which the hypothenuse is the distance between the initial and final point. Therefore, the distance can be found by using Pythagorean's theorem:
So, 4.47 blocks.
2)
The horizontal and vertical components of the vector can be calculated as
where
v = 41 N is the magnitude of the vector
is the angle between the direction of the vector and the x-axis (which corresponds to the east direction)
Substituting numbers into the equations, we find
3)
In the previous part, we said that the horizontal component of a vector is given by
where
v is the magnitude of the vector
is the angle
In this problem we know that:
is the horizontal component
is the angle
Therefore, we can re-arrange the equation to find v, the magnitude of the resultant vector:
Learn more about vectors here:
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