A car is driven east for a distance of 46 km, then north for 27 km, and then in a direction 35° east of north for 24 km.
Determine the angle (from east) of the car's total displacement measured from its starting direction.
35 Deg. E of N = 90 - 35 = 55 Deg CCW
from the positive x-axis.
X = Hor = 46 + 24cos55 = 46 + 13.6 = 59.8 km.
Y = Ver. = 27 + 24sin55 = 27 + 19.7 =
46.7 km.
D = (59.8 - 46) + i46.7 = 13.8 + i46.7
tanA = 46.7/13.8 = 3.38,
A = 73.5 Deg. = Angle of Displacement.
To determine the angle (from east) of the car's total displacement, we can use the concept of vector addition.
First, let's break down the car's displacement into its eastward component and northward component.
1. Eastward Component:
The car is driven east for a distance of 46 km, so the eastward component is 46 km.
2. Northward Component:
The car then moves north for a distance of 27 km, so the northward component is 27 km.
Next, we need to find the resultant displacement by adding the eastward and northward components. To do this, we can use trigonometry.
3. Calculating the Resultant Displacement:
Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement:
Resultant Displacement (R) = √(eastward component^2 + northward component^2)
R = √(46^2 + 27^2) = √(2116 + 729) = √2845 ≈ 53.34 km
4. Finding the Angle (from east) of the Car's Total Displacement:
To find the angle (from east) of the car's total displacement, we can use trigonometric ratios. We want to calculate the angle θ, which is the angle between the eastward direction and the resultant displacement.
We can use the inverse tangent function to find θ:
tan(θ) = (northward component / eastward component)
θ = atan(northward component / eastward component)
θ = atan(27 / 46) ≈ 30.96°
Therefore, the angle (from east) of the car's total displacement is approximately 30.96°.