3. Vectors

A cyclist travels $3$ km east and then $4$ km north. What is the straight-line distance from the starting point to the cyclist's final position?

An object is placed in front of a thin converging lens. Which of the following statements correctly describes the nature of the image formed when the object is located at a distance greater than twice the focal length from the lens?$d>2f$

Which vector quantity was historically used to help sailors determine direction at sea?

An underwater diver sees the sun at an angle of $60°$ above the horizontal. Assuming the refractive index of water is $1.33$ and that of air is $1.00$, what is the actual angle of elevation of the sun above the horizontal as seen by an observer in air?

Which of the following physical systems is best modeled as a cylindrical pipe with both ends open, similar to the clarinet?

Which of the following best describes how to determine the net displacement vector for the beam constructed from four pieces of wood joined end-to-end as shown in Figure 1?

Two solid cylindrical rods AB and BC are joined end to end to form a straight rod. If the cross-sectional area of rod AB is $A$ and that of rod BC is $2A$, and both are made of the same material, which statement about the magnitude of the force required to produce the same extension in each rod is correct?

Given the vector field $f(x,y,z)=(x\cos (y),x{y}^2,0)$, what is $\nabla \times f$ (the curl of $f$)?

Compared to a solid wire of the same gauge, which of the following statements about a stranded wire is correct?

Which of the following is a vector quantity?

Which statement about $vectors$ is true?

Two perpendicular forces act on a box, one pushing to the right and one pushing up. An instrument tells you the magnitude of the total force is 13N. You measure the force pushing to the right is 12N. Calculate the force pushing up.