A woman using a compass and a map walks 132 degrees east of north for 6 km. Find the components of the woman's displacement.
A. Ax = 4.46 km, Ay = 4.01 km
B. Ax = 0.74 km, Ay = -0.67
C. Ax = 4.46 km, Ay = -4.01 km
D. Ax = 0.74 km, Ay = 0.67 km
(I'm new to this and somewhat confused. I think the answer's C though...) Someone please help...
is y North, x east? 132 deg E of N is not a common description, since the angle would normally be written as 42 deg S of E. Assuming so
Ax=6*sin 132=4.46km
Ay=6*cos132=-4.01km
Why did the woman bring a compass and a map to her walk? Did she think she was going on a treasure hunt? Anyway, let's get back to the question: calculating the components of her displacement. To do that, we need to break her displacement vector into horizontal and vertical components.
Given that she walks 132 degrees east of north, we know that her horizontal displacement is 6 km times the cosine of 132 degrees, and her vertical displacement is 6 km times the sine of 132 degrees.
Using a bit of trigonometry and some calculation, we find:
Ax = 6 km * cos(132 degrees) = 4.46 km
Ay = 6 km * sin(132 degrees) = -4.01 km
So, it looks like option C is indeed the correct answer!
To find the components of the woman's displacement, we can use trigonometry.
First, we need to determine the angle between the displacement vector and the positive x-axis. Since the woman is walking 132 degrees east of north, we need to subtract this angle from 90 degrees to get the angle measured from the positive x-axis.
The angle measured from the positive x-axis = 90 degrees - 132 degrees = -42 degrees.
Next, we can use the angle and the length of the displacement to find the x-component and y-component of the displacement.
The x-component of the displacement = Displacement * cos(angle)
The y-component of the displacement = Displacement * sin(angle)
Using the given values:
Angle = -42 degrees
Displacement = 6 km
The x-component of the displacement = 6 km * cos(-42 degrees) = 4.46 km
The y-component of the displacement = 6 km * sin(-42 degrees) = -4.01 km
Therefore, the components of the woman's displacement are:
Ax = 4.46 km and Ay = -4.01 km
So the correct answer is C.
To find the components of the woman's displacement, we can break it down into its horizontal and vertical components.
First, let's draw a diagram to visualize the situation. Draw a coordinate system with North as the positive y-axis and East as the positive x-axis. The woman walks 132 degrees east of north, so her displacement makes an angle of 132 degrees with the positive y-axis.
Now, let's find the components. The horizontal component, Ax, represents the displacement in the x-direction (east), and the vertical component, Ay, represents the displacement in the y-direction (north). We can use trigonometry to find these components.
To find Ax, we can use the cosine function. The cosine of the angle between the displacement vector and the y-axis gives us the ratio of the horizontal displacement to the total displacement.
Ax = 6 km * cos(132 degrees)
Ax ≈ 6 km * (-0.742)
Ax ≈ -4.452 km
To find Ay, we can use the sine function. The sine of the angle between the displacement vector and the y-axis gives us the ratio of the vertical displacement to the total displacement.
Ay = 6 km * sin(132 degrees)
Ay ≈ 6 km * (0.670)
Ay ≈ 4.020 km
So, the components of the woman's displacement are approximately Ax = -4.452 km and Ay = 4.020 km.
Therefore, the correct answer is C. Ax = -4.452 km, Ay = 4.020 km.