Question

A ladybug starts at the center of a 16.0in.-diameter turntable and crawls in a straight radial line to the edge. While this is happening, the turntable turns through a 30.0degree angle.

A) Find the magnitude of the ladybug's displacement vector.
B) Find the direction of the ladybug's displacement vector. Please express your answer as an angle between the displacement vector and the initial direction of the motion.

Answer 1

A ladybug starting at the center of a 16.0in.-diameter turntable crawls to the edge while it turns through a 30.0 degree angle. The magnitude of the ladybug's displacement vector is approximately 50.27 inches and the direction of the displacement vector is perpendicular to the angle of rotation.

Step-by-step explanation:

A) To find the magnitude of the ladybug's displacement vector, we need to calculate the distance it traveled from the center to the edge of the turntable. Since the turntable has a diameter of 16.0 inches, the radius is half of that, which is 8.0 inches. Using the formula for the circumference of a circle, C = 2πr, we can find that the distance traveled by the ladybug is about 2π(8.0) = 16π inches, which is approximately 50.27 inches.

B) To find the direction of the ladybug's displacement vector, we consider the angle through which the turntable turns. Since the turntable turns through a 30.0-degree angle, the direction of the ladybug's displacement vector is perpendicular to this angle. Therefore, the angle between the displacement vector and the initial direction of motion is 90 degrees.

Answer 2

A) 8.00 in B)30.0° from initial direction

Step-by-step explanation:

A)

The Diameter of the turntable is 16 inch so the radius

r = D/2 = 16/2 = 8 inches

Since the lady bug moves from the center to the edge, the displacement is equal to the radius in magnitude

S = r = 8 inches

B)

Let us say the lady bug is moving in positive x axis initially, so the lady bug must have moved an angle of 30° degrees when it reached the edge of the turntable.

θ = 30° - 0°

θ = 30°