Question

A car travels 200 m to the east, then 500 m north-east and finally 100 m east to reach its destination. Find the north component of the car's trip.

a) 200 m
b) 400 m
c) 300 m
d) 500 m

Answer 1

The north component of the car's trip is approximately 354 m.

Step-by-step explanation:

To find the north component of the car's trip, we need to break down the car's movement into its east and north components. Initially, the car travels 200 m to the east, which does not contribute to the north component. Then, the car travels 500 m northeast. We can find the north component of this movement by multiplying the total distance traveled (500 m) by the sine of the angle between the northeast direction and the north direction (45° minus 0°):

North component = 500 m × sin(45° - 0°) = 500 m × sin(45°) ≈ 354 m

Finally, the car travels 100 m directly east, again not contributing to the north component. Therefore, the north component of the car's trip is approximately 354 m.