A figure skater glides along a circular path of radius 5.20 m.
(a) If she coasts around one half of the circle, find the magnitude of the displacement vector.
m
(b) If she coasts around one half 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 solve these questions, we need to understand the concepts of displacement and distance, as well as how they relate to each other.
Displacement refers to the change in position of an object from its initial position to its final position. It is a vector quantity, meaning it has both magnitude and direction. Displacement is represented by a vector.
Distance refers to the total length of the path traveled by an object. It is a scalar quantity, meaning it only has magnitude and no direction. Distance is represented by a scalar.
Okay, let's solve each question step by step:
(a) To find the magnitude of the displacement vector when the skater coasts around one half of the circle, we need to calculate the length of the half-circumference of the circle.
The formula for the circumference of a circle is given by:
Circumference = 2π × radius
In this case, the radius of the circle is given as 5.20 m. So, the half-circumference would be:
Half-Circumference = (1/2) × 2π × radius = π × radius
Substituting the radius value into the formula, we get:
Half-Circumference = π × 5.20 m
Now, the magnitude of the displacement vector is equal to the half-circumference since the skater returns back to the starting point after completing half of the circle. Therefore,
Magnitude of Displacement = Half-Circumference = π × 5.20 m ≈ 16.34 m
So, the magnitude of the displacement vector when the skater coasts around one half of the circle is approximately 16.34 m.
(b) To find the distance the skater skated when coasting around one half of the circle, we simply need to calculate the half-circumference of the circle using the formula mentioned earlier:
Distance = Half-Circumference = π × 5.20 m ≈ 16.34 m
So, the distance the skater skated when coasting around one half of the circle is approximately 16.34 m.
(c) To find the magnitude of the displacement when the skater skates all the way around the circle, we need to calculate the entire circumference of the circle:
Circumference = 2π × radius = 2π × 5.20 m
The magnitude of the displacement when the skater skates all the way around the circle is equal to the circumference since she comes back to the starting point. Therefore,
Magnitude of Displacement = Circumference = 2π × 5.20 m
Now, you can simplify this expression using the value of π (approximately 3.14) and calculate the result.
Remember, it's important to note that displacement is a vector quantity and has both magnitude and direction, while distance is a scalar quantity and only has magnitude.