Answer:
Step-by-step explanation:
In order to find the magnitude of the car's final displacement (resultant displacement vector), we need the x and y components of each part of the car's journey. We will call them vector A and vector B. The info for the vectors is as follows:
A: magnitude 32 at an angle of 90.0
B: magnitude 46 at an angle of 40.0
The x components are found in the formula
A(x) = magA*cos(angle)
For A(x):
A(x) : 32cos(90.0) = 0.0 and
For B(x) : 46cos(40.0) = 35.2
For A(y): 32sin(90.0) = 32 and
For B(y): 46sin(40.0) = 3.0 × 10¹
To get the x components of the final vector, add the x components of A and B together:
C(x) : 0.0
35.2
35.2
To get the y components of the final vector, add the y components of A and B together:
C(y) : 32
30
62
Now to get the magnitude, throw it into the magnitude formula, which is identical to Pythagorean's theorem:
C(mag) = [tex]\sqrt{(35.2^2)+(62^2)}=71.3 km[/tex]
