A circular test track for cars has a circumference of 2.1 km . A car travels around the track from the southernmost point to the northernmost point
what distance does the car travel?
So to find displacement from the southernmost part to the northernmost part of the track you divide the circumference by 2 so 2.1/2 which gives 1.05 as shown above. Now to find the total displacement from origin you have to do some arithmetic. circle's circumference is (2piR = 2.1) from this you find r and since you started from the south part and went till north you multiple the radius by two (to get diameter). This would make sense if you draw out a car track (circle) and follow along with it with the question. Also, a shortcut would be to just have your circumference divided by pi and set that = d(since that is what we are trying to find in this specific question) 2.1/pi = .67 km. So .67km is the answer to this question. Hope all that extra explanaiton helps others with different values.
2.1 / 2 = ______ km
I got it it was 2.1 x .5 then i calculated it now I am trying to figure out What the car's displacement is from its original position?
how would I figure that out do I divide from the 2.1 and the 1.05?
To find the distance the car travels, we need to determine the length of the arc between the southernmost and northernmost points of the circular track.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, we are given the circumference, C = 2.1 km.
To find the radius, we can rearrange the formula to solve for r:
r = C / (2π)
Substituting the given circumference, we have:
r = 2.1 km / (2π)
Next, we need to find the length of the arc between the two points. The formula for the length of an arc is:
l = θ/360° * 2πr
where l is the length of the arc, θ is the angle subtended by the arc at the center, and r is the radius.
Since the car travels from the southernmost to the northernmost point, it covers half of the circumference, which is 180°.
Plugging in the values, we have:
l = 180°/360° * 2π * (2.1 km / (2π))
Simplifying the equation, we get:
l = (180/360) * 2.1 km
Finally, we can solve for the length of the arc:
l = 1 * 2.1 km
Therefore, the distance the car travels from the southernmost point to the northernmost point on the circular track is 2.1 km.