K A Tsokos Solutions for Chapter: Measurement and Uncertainties, Exercise 3: Test yourself

A body is acted upon by the two forces shown in the diagram. In each case draw the one force whose effect on the body is the same as the two together.

The position vector of a moving object has components $(r_x=2 \mathrm{unit}, r_y=2 \mathrm{unit})$ initially. After a certain time the position vector has components $(r_x=4 \mathrm{unit}, r_y=8 \mathrm{unit})$. Find the displacement vector.

The diagram shows the velocity vector of a particle moving in a circle with speed $10 \mathrm{m} {\mathrm{s}}^{-1}$ at two separate points. The velocity vector is tangential to the circle. Find the vector representing the change in the velocity vector.

In a certain collision, the momentum vector of a particle changes direction but not magnitude. Let $p$ be the momentum vector of a particle suffering an elastic collision and changing direction by $30°$. Find, in terms of $p(=|p\left|\right)$, the magnitude of the vector representing the change in the momentum vector:

Vector $A$ has a magnitude of $6.00 \mathrm{units}$ and is directed at $60°$ to the positive x-axis. Vector $B$ has a magnitude of $6.00 \mathrm{units}$ and is directed at $120°$ to the positive x-axis. Find the magnitude and direction of vector $C$ such that $A+B+C=0$. Place the three vectors so that one begins where the previous ends. What do you observe?