1. A body is moving along a circular path of radius R. What will be the distance covered and the displacement of the body after half a revolution?
2. A person starts from his house and travels a circular distance of 15 km around the walled city before returning back. What is (a) distance covered by the person, (b) the displacement of the person?
a. what is PI*radius?
b. distance is 15km. Displacement is zero.
1. To find the distance covered by the body after half a revolution on a circular path of radius R, we first need to calculate the circumference of the circle. The formula for the circumference of a circle is given by:
C = 2 * π * R
where C is the circumference and R is the radius of the circle.
In this case, since the body has completed half a revolution, it has traveled half the circumference of the circle. Therefore, we multiply the circumference by 0.5 to get the distance covered:
Distance covered = 0.5 * C
= 0.5 * (2 * π * R)
= π * R
So, the distance covered by the body after half a revolution is π * R.
To find the displacement of the body, we consider that displacement is the straight-line distance between the initial and final positions. Since the body has completed half a revolution, its initial and final positions will be diametrically opposite on the circle.
The diameter of the circle is given by:
Diameter = 2 * R
Therefore, the displacement is equal to the diameter of the circle:
Displacement = Diameter
= 2 * R
So, the displacement of the body after half a revolution is 2 * R.
2. To calculate the distance covered by the person when they travel a circular distance of 15 km around the walled city before returning back, we can use the formula for the circumference:
C = 2 * π * R
Here, we know that the circumference is 15 km. We can rearrange the formula to solve for the radius:
R = C / (2 * π)
= 15 km / (2 * π)
Once we have the radius, we can calculate the distance covered by using the formula:
Distance covered = Circumference
= 2 * π * R
= 2 * π * (15 km / (2 * π))
= 15 km
So, the distance covered by the person is 15 km.
To calculate the displacement of the person, we need to know the starting and ending points. Since the person ends up back at their house, the starting and ending points are the same.
The displacement is the straight-line distance between the starting and ending points, which is zero in this case. Therefore, the displacement of the person is 0 km.