A figure skater glides along a circular path of radius 4.70 m.

(a) If she coasts around one fourth of the circle, find the magnitude of the displacement vector.
m

(b) If she coasts around one fourth of the circle, find what distance she skated.
m

(c) What is the magnitude of the displacement if she skates all the way around the circle?
m

I will be happy to critique your work.

To answer these questions, we need to understand the concepts of displacement and distance.

Displacement refers to the change in position of an object, including its direction, from its initial position to its final position. It is represented by a vector and can be positive, negative, or zero.

Distance, on the other hand, refers to the actual path taken by an object from its initial position to its final position. It is a scalar quantity and is always positive or zero since it represents the length of the path traveled.

Now, let's tackle each question:

(a) To find the magnitude of the displacement vector when the skater coasts around one fourth of the circle, we need to determine the change in position. In other words, we need to find the distance between the initial and final positions.

Since the skater is moving along a circular path of radius 4.70 m, one fourth of the circle would be 1/4 times the circumference of the circle. The circumference of a circle is given by 2πr, where r is the radius.

Circumference = 2π(4.70 m) = 29.56 m

One fourth of the circumference = 1/4 × 29.56 m = 7.39 m

So, the magnitude of the displacement vector is 7.39 m.

(b) To find the distance the skater skated when coasting around one fourth of the circle, we simply need to consider the length of the path along the circle.

Since one fourth of the circumference is 7.39 m, the skater traveled a distance of 7.39 m.

(c) If the skater skates all the way around the circle, the distance traveled would be equal to the circumference of the circle, which, as mentioned earlier, is 2πr. Plugging in the values, we get:

Circumference = 2π(4.70 m) = 29.56 m

Therefore, the magnitude of the displacement when the skater skates all the way around the circle is 29.56 m.

In conclusion:
(a) The magnitude of the displacement vector when the skater coasts around one fourth of the circle is 7.39 m.
(b) The distance the skater skated when coasting around one fourth of the circle is 7.39 m.
(c) The magnitude of the displacement if the skater skates all the way around the circle is 29.56 m.

looking at your posts, are you taking a test? cheating?