Answer:
about 2.9° north of east
Step-by-step explanation:
If we orient the directions so north is in the +y direction and east is in the +x direction, the car is traveling 13 km at an angle of -45°, then 16 km at an angle of +40°. We can add these vectors by adding their components in the x- and y-directions.
13(cos(-45°), sin(-45°)) ≈ (9.19239, -9.19239)
16(cos(40°), sin(40°)) ≈ (12.25671, 10.28460)
The sum of these vectors is then ...
= (21.44910, 1.09221)
and the resultant angle is ...
arctan(1.09221/21.44910) ≈ 2.915° . . . . measured north of east
The resultant direction is about 2.9° north of east.
Answer:
Magnitude of resultant direction = 3.253 Km
Direction of resultant motion = 19.62° North of East
Step-by-step explanation:
Here we have
13 km in SE direction and
16 km 40 ° North of East
Therefore
13 cos 45, 13 sin 45 = (9.192, 9.9192)
16 cos 40, 16 sin 40 = (12.2567, 10.245)
x₂ - x₁ = 3.064
y₂ - y₁ = 1.092
The Magnitude = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex] = 3.253
The direction = Arctan (y₂ - y₁)/(x₂ - x₁) = Arctan 1.092/3.064 = 19.62° North of East
