A car travels 2.92 km in the x-direction, then turns left 75.8◦ to the original direction and travels an additional distance of 1.71 km.

Calculate the x component of the car’s net displacement.
Let:
d1 =2.92km,
θ = 75.8◦ , and
d2 = 1.71 km .

answer in units of km

Disp. = d1 [0o] + d2[75.8o].

Disp. = 2.92km[0o] + 1.71km[75.8o].
X = 2.92*Cos 0 + 1.71*Cos75.8 =

To find the x-component of the car's net displacement, we need to determine the horizontal distance traveled by the car.

We can break down the car's displacement into two components: the x-component and the y-component. The x-component represents the distance traveled in the x-direction, and the y-component represents the distance traveled in the y-direction.

Given:
d1 = 2.92 km (distance traveled in the x-direction)
θ = 75.8◦ (angle turned left from the original direction)
d2 = 1.71 km (additional distance traveled in the new direction)

To find the x-component of the car's net displacement, we can first calculate the horizontal distance traveled (d_x) using trigonometry.

Using the given angle θ, we can find the y-component (d_y) of the car's displacement using the formula:
d_y = d1 * sin(θ)

Next, we can find the x-component (d_x) using the formula:
d_x = d1 * cos(θ) + d2

Let's plug in the values:
d_y = 2.92 km * sin(75.8°)
d_x = 2.92 km * cos(75.8°) + 1.71 km

Calculating:
d_y = 2.92 km * 0.9661
d_y = 2.824412 km (rounded to 6 decimal places)

d_x = 2.92 km * 0.2575 + 1.71 km
d_x = 0.7511 km + 1.71 km
d_x = 2.4611 km

The x component of the car's net displacement is 2.4611 km.