A car travels 2.06 km in the x-direction, then
turns left 70.3 degrees to the original direction and
travels an additional distance of 4.23 km.
Calculate the x component of the car’s net
displacement.
Let :
d1 = 2.06 km,
theta = 70.3 degrees , and
d2 = 4.23 km.
To calculate the x component of the car's net displacement, we need to break down the displacement into horizontal and vertical components.
First, let's calculate the horizontal component of the displacement. The car initially travels 2.06 km in the x-direction, so its x component is 2.06 km.
Next, let's calculate the vertical component of the displacement. The car turns left 70.3 degrees to the original direction, which means it changes its y-direction. Since the car only travels in the x and y directions, this means that after the turn, the car will have some displacement in both the x and y directions.
To calculate the vertical component, we need to determine the change in position in the y-direction. We know that the magnitude of the displacement in the y-direction is equal to d2 (4.23 km). To find the actual vertical displacement, we need to calculate the sine of the angle theta and then multiply it by d2.
So, the vertical component (y) can be calculated as follows:
y = sin(theta) * d2
Now, let's plug in the values we have:
theta = 70.3 degrees
d2 = 4.23 km
Using a calculator, we can find the value of sin(70.3 degrees). Let's say sin(70.3 degrees) = 0.9397 (rounded to four decimal places).
Therefore, the vertical component (y) is:
y = 0.9397 * 4.23 km = 3.98 km (rounded to two decimal places)
Since the car only changes its y-direction but continues to travel in the x-direction, the x component of the car's net displacement is the same as its initial x component. Therefore, the x component of the car's net displacement is:
x = 2.06 km
So, the x component of the car's net displacement is 2.06 km.