A car travels 1.72 km in the x direction, then turns left 50.4 degrees to the original direction and travels an additional distance of 1.97 km. Calculate the x component of the car's net displacement. Answer in units of km.

Isn't this a lot like the prior two? break each leg into x components, and add.

To calculate the x component of the car's net displacement, we need to break down the total displacement into its x and y components.

First, let's calculate the x component of the initial displacement. The car travels 1.72 km in the x direction, so the x component of the initial displacement is simply 1.72 km.

Next, we need to find the x component of the displacement after the car turns left. To do this, we can use the formula: x = d * cos(theta), where d is the magnitude of the displacement and theta is the angle between the displacement and the positive x-axis.

The magnitude of the displacement after the turn is 1.97 km. The angle of the turn is 50.4 degrees. Plugging these values into the formula, we get:

x = 1.97 km * cos(50.4 degrees)

Now, we can use a calculator to find the cosine of 50.4 degrees and multiply it by 1.97 km to get the x component of the displacement after the turn.

x = 1.97 km * cos(50.4 degrees) ≈ 1.26 km

Finally, to find the x component of the car's net displacement, we need to add the x components of the initial and final displacements:

x_net = 1.72 km + 1.26 km = 2.98 km

Therefore, the x component of the car's net displacement is approximately 2.98 km.