A women walks 250m in the diretuibn 30 degrees east of north, then 175m east.
a)what is the magnitude and angel of her final displacement from the starting point?
I should be getting 370m and 36 degrees north of east but I keep on getting the wrong answers.
East: 250Sin30 + 175
North: 240cos30
240
All angles are measured CCW from +x-axis.
Disp. = 250m[60o] + 175m[0o].
Disp. = (250*Cos60+i250*sin60) + 175.
Disp. = 125+216.5i + 175 = 300 + 216.5i = 370m[36o].
To find the magnitude and angle of the final displacement, we can break it down into the East and North components.
First, let's calculate the East component. The woman walks 250 meters in the direction 30 degrees east of north. To find the eastward component, we will use the formula:
East = Magnitude * cos(Angle)
East = 250 * cos(30)
East ≈ 250 * 0.866
East ≈ 216.5 meters
Next, let's calculate the North component. The woman then walks 175 meters east. To find the northward component, we will use the formula:
North = Magnitude * sin(Angle)
North = 175 * sin(90)
North = 175 meters
Now, we have the East component of 216.5 meters and the North component of 175 meters. To find the magnitude of the final displacement, we can use the Pythagorean theorem:
Magnitude (Displacement) = sqrt(East^2 + North^2)
Magnitude ≈ sqrt(216.5^2 + 175^2)
Magnitude ≈ sqrt(46922.25 + 30625)
Magnitude ≈ sqrt(77547.25)
Magnitude ≈ 278.5 meters
Lastly, to find the angle of the final displacement, we can use the inverse tangent function:
Angle (Displacement) = atan(East / North)
Angle ≈ atan(216.5 / 175)
Angle ≈ atan(1.236)
Angle ≈ 50.2 degrees
Therefore, the magnitude of the final displacement is approximately 278.5 meters, and the angle is approximately 50.2 degrees.