Answer:
So the car's velocity can be broken down into a component of 17.32 m/s due North and 10 m/s due West.
Step-by-step explanation:
To calculate the components of the car's velocity due North and due West, we need to use trigonometry. The car is travelling at N 30° W, which means it is moving in a direction that is 30 degrees west of north. This can be represented by a vector pointing in that direction, with a magnitude of 20 m/s.
To find the component of the car's velocity due North, we need to find the length of the line that runs perpendicular to the direction of motion and intersects with the North-South axis. This is the adjacent side of a right triangle, with the hypotenuse being the car's velocity vector and the angle between the adjacent side and the hypotenuse being 30 degrees.
Using trigonometry, we can calculate the length of the adjacent side as follows:
cos(30°) = adjacent/hypotenuse
adjacent = cos(30°) x 20 m/s
adjacent = 17.32 m/s
Therefore, the component of the car's velocity due North is 17.32 m/s.
To find the component of the car's velocity due West, we need to find the length of the line that runs perpendicular to the direction of motion and intersects with the East-West axis. This is the opposite side of the right triangle we used earlier.
Using trigonometry, we can calculate the length of the opposite side as follows:
sin(30°) = opposite/hypotenuse
opposite = sin(30°) x 20 m/s
opposite = 10 m/s
Therefore, the component of the car's velocity due West is 10 m/s.
So the car's velocity can be broken down into a component of 17.32 m/s due North and 10 m/s due West.