A bus travels 25.0 km on a straight road that is 30° north of east
To determine the distance traveled by the bus on a straight road that is 30° north of east, we can break down the displacement into its northward and eastward components.
First, we calculate the eastward distance traveled.
Using trigonometry, we can find the eastward component of the displacement. The eastward distance can be calculated by multiplying the total distance traveled by the cosine of the angle of the road.
Eastward distance = Total distance * cos(angle)
Eastward distance = 25.0 km * cos(30°)
Eastward distance ≈ 25.0 km * 0.866
Eastward distance ≈ 21.65 km
Then, we calculate the northward distance traveled.
Similarly, the northward distance can be calculated by multiplying the total distance traveled by the sine of the angle of the road.
Northward distance = Total distance * sin(angle)
Northward distance = 25.0 km * sin(30°)
Northward distance ≈ 25.0 km * 0.5
Northward distance ≈ 12.5 km
Thus, the bus travels approximately 21.65 km eastward and 12.5 km northward on the straight road.