Chapter 1

Find the magnitude and direction of $-5\overrightarrow{A}+\overrightarrow{B},$ where $\overrightarrow{A}=(23.0,59.0),\overrightarrow{B}=(90.0,-150.0)$

Find the magnitude and direction of $-7\overrightarrow{B}+3\overrightarrow{A}$, where $\overrightarrow{A}=(23.0,59.0),\overrightarrow{B}=(90.0,-150.0)$

Find the magnitude and direction of (a) $9\overrightarrow{B}-3\overrightarrow{A}$ and (b) $-5\overrightarrow{A}+8\overrightarrow{B},$ where $\overrightarrow{A}=(23.0,59.0),\overrightarrow{B}=(90.0,-150.0)$

Express the vectors $A=(A_x,A_y)=(-30.0\mathrm{m},-50.0\mathrm{m})$ and $\overrightarrow{B}=(B_x,B_y)=(30.0\mathrm{m},50.0\mathrm{m})$ by giving their magnitude and direction as measured from the positive $x$ -axis.

The force $F$ a spring exerts on you is directly proportional to the distance $x$ you stretch it beyond its resting length. Suppose that when you stretch a spring $8.00\mathrm{cm},$ it exerts a 200. N force on you. How much force will it exert on you if you stretch it $40.0\mathrm{cm}?$

The distance a freely falling object drops, starting from rest, is proportional to the square of the time it has been falling. By what factor will the distance fallen change if the time of falling is three times as long?

A pilot decides to take his small plane for a Sunday afternoon excursion. He first flies north for 155.3 miles, then makes a ${90}^{\circ }$ turn to his right and flies on a straight line for 62.5 miles, then makes another ${90}^{\circ }$ turn to his right and flies 47.5 miles on a straight line. a) How far away from his home airport is he at this point? b) In which direction does he need to fly from this point on to make it home in a straight line? c) What was the farthest distance he was away from the home airport during the trip?

A hiker travels $1.50\mathrm{km}$ north and turns to a heading of ${20.0}^{\circ }$ north of west, traveling another $1.50\mathrm{km}$ along that heading. Subsequently, he then turns north again and travels another $1.50\mathrm{km}.$ How far is he from his original point of departure, and what is the heading relative to that initial point?

Assuming that 1 mole $(6.02\cdot {10}^{23}$ molecules) of an ideal gas has a volume of $22.4\mathrm{L}$ at standard temperature and pressure (STP) and that nitrogen, which makes up $80.0\mathrm{\%}$ of the air we breathe, is an ideal gas, how many nitrogen molecules are there in an average $0.500\mathrm{L}$ breath at STP?

On August 27,2003 , Mars approached as close to Earth as it will for over 50,000 years. If its angular size (the planet's radius, measured by the angle the radius subtends) on that day was measured by an astronomer to be 24.9 seconds of arc, and its radius is known to be $6784\mathrm{km}$, how close was the approach distance? Be sure to use an appropriate number of significant figures in your answer.