(II) You look directly overhead and see a plane exactly 1.25 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. Determine the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s.

The power generated by a windmill is a function of the speed of the wind. The approximate power is given by the function $P(s)=\frac{s^3}{1000^{\prime}}$, where s represents the speed of the wind in kilometers per hour. Find the units of power P(s) generated by a windmill when the wind speed is 18 kilometers per hour.

An investigation of a number of automobile accidents revealed the following information: a. 18 accidents involved alcohol and excessive speed. b. 26 accidents involved alcohol. c. 12 accidents involved excessive speed but not alcohol. d. 21 of the accidents involved neither alcohol nor excessive speed. State how many accidents were investigated.

A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to determine the speed of the current.

What is the speed of a 4kg ball with the momentum of $12\:\text{kg}$?

A $20 \mathrm{~g}$ ball is fired horizontally with speed $v_0$ toward a $100 \mathrm{~g}$ ball hanging motionless from a 1.0-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the $100 \mathrm{~g}$ ball swings out to a maximum angle $\theta_{\max }=50^{\circ}$. What was $\nu_0$ ?

An observer at rest on the ground sees a jet plane fly overhead at a constant speed of $2000 \mathrm{~km} \mathrm{~h}^{-1}$. At what speed does the pilot see the ground moving?

You have measured speed in terms of the lengths of paper tape. A quick and portable way of representing the paper-tape graphs you made is by drawing graphs of the data. The four graphs labeled $\mathrm{A}-\mathrm{D}$ are histograms. Each bar on the histogram represents a piece of cut paper tape.

a) Which graph(s) represent(s) a student moving with a constant increase in speed?

b) Which graph(s) represent(s) a student moving with a constant speed?

c) Which graph indicates the greatest change in speed each second?

d) Which graph(s) represent(s) the motion of a student whose speed first increased but later decreased?

e) The acceleration of an object is defined as the change in speed of the object per second. What is the acceleration of the student in $\mathrm{A}$ ? In B? In C? In D?

Studies by the Federal Highway Administration suggest that speed limits on many thoroughfares are set arbitrarily, and are often artificially low. According to traffic engineers, the ideal speed limit should be the 85 th percentile speed. This means the speed at or below which 85 percent of the traffic moves. Assuming speeds are normally distributed, find the 85 th percentile speed for roads with the following conditions. Source: Federal Highway Administration.

The mean speed is $30 \mathrm{mph}$ with a standard deviation of $5 \mathrm{mph}$.

A projectile is fired with an initial speed of 200 m/s and angle of elevation $60^{\circ}$. Find the speed at impact.

Giovanni is flying his Cessna airplane on a heading as shown. His instrument panel shows an air speed of 130 mi/h. (Air speed is the speed in still air without wind.) However, there is a 20 mi/h crosswind. What is the resulting speed of the plane?

Driving time varies inversely as speed. If it takes 3 hours to drive to the beach at an average speed of 48 mph, how long will it take to drive home at an average speed of 54 mph?

Studies by the Federal Highway Administration suggest that speed limits on many thoroughfares are set arbitrarily, and are often artificially low. According to traffic engineers, the ideal speed limit should be the 85 th percentile speed. This means the speed at or below which 85 percent of the traffic moves. Assuming speeds are normally distributed, find the 85 th percentile speed for roads with the following conditions. Source: Federal Highway Administration.

The mean speed is $52 \mathrm{mph}$ with a standard deviation of $8 \mathrm{mph}$.

A ball rolls on the ground at a speed of 3.0 m/s without slipping. If the radius of the ball is 10 cm, what is the angular speed of the ball?