Wood bats are required in professional baseball but metal bats are sometimes allowed in youth and college baseball. One result is that the exit speed $v$ of the baseball off a metal bat can be greater. In one set of measurements under the same circumstances, $v=50.98 \mathrm{~m} / \mathrm{s}$ off a wood bat and $v=61.50 \mathrm{~m} / \mathrm{s}$ off a metal bat. Consider a ball hit directly toward the pitcher. The regulation distance between pitcher and batter is $\Delta x=60 \mathrm{ft} 6 \mathrm{in}$. For those measured speeds, how much time $\Delta t$ does the ball take to reach the pitcher for $(a)$ the wood bat and $(b)$ the metal bat? $(c)$ By what percentage would $\Delta t$ be reduced if professional baseball switched to metal bats? Because pitchers do not wear any protective equipment on face or body, the situation is already dangerous and the switch would add to that danger.

When freeways were first built in the United States in the $1950$s, entrance ramps were often too short for an entering car to safely merge into existing traffic. Consider an aggressive car acceleration of $a=4.0 \mathrm{~m} / \mathrm{s}^2$ and an initial car speed of $v_0=25 \mathrm{mi} / \mathrm{h}$ as the car enters the entrance ramp of a freeway where other cars are moving at $55 \mathrm{mi} / \mathrm{h}$. $(a)$ If the ramp has a length of $d=40 \mathrm{yd}$, what is the car's speed $v$ in miles per hour as it attempts to merge? $(b)$ What is the minimum length $d$ in yards needed for the car's speed to match the speed of the other cars?

The greatest speed limit in the United States is along the tolled section of Texas State Highway 130 where the limit is $85 \mathrm{mi} / \mathrm{h}$. How much time would be saved in driving that $41 \mathrm{mi}$ section at the speed limit instead of $60 \mathrm{mi} / \mathrm{h}$ ? (b) The speed limit in residential areas is commonly $25 \mathrm{mi} / \mathrm{h}$ but some motorists drive at an average speed of $45 \mathrm{mi} / \mathrm{h}$, perhaps by weaving through traffic and even driving through traffic lights that had just turned red. How much time would be saved in driving at that faster speed through $5.5 \mathrm{mi}$ instead of the posted speed limit if the car does not stop at any intersections?

The running event known as the $100 \mathrm{~m}$ dash consists of three stages. In the first, the runner accelerates to the maximum speed, which usually occurs at the $50 \mathrm{~m}$ to $70 \mathrm{~m}$ mark. That speed is then maintained until the last $10 \mathrm{~m}$, when the runner slows. Consider three parts of the record-setting run by Usain Bolt in the $2008$ Olympics: $(a)$ from $10 \mathrm{~m}$ to $20 \mathrm{~m}$, elapsed time of $1.02 \mathrm{~s}$, $(b)$ from $50 \mathrm{~m}$ to $60 \mathrm{~m}$, elapsed time of $0.82 \mathrm{~s}$, and $(c)$ from $90 \mathrm{~m}$ to $100 \mathrm{~m}$, elapsed time of $0.90 \mathrm{~s}$. What was the average velocity for each part?

In professional baseball, the pitching distance of $60$ feet $6$ inches is the distance from the front of the pitcher's plate (or rubber) to the rear of the home plate. $(a)$ Assuming that a $95 \mathrm{mi} / \mathrm{h}$ fastball travels that full distance horizontally, what is its flight time, which is the time a batter must judge if the ball is "hittable" and then swing the bat? $(b)$ Research indicates that even an elite batter cannot track the ball for the full flight and yet many players have described seeing the ball-bat collision. One explanation is that the eyes track the ball in the early part of the flight and then undergo a predictive saccade in which they jump to an anticipated point later in the flight. A saccade suppresses vision for $20 \mathrm{~ms}$. How far in feet does the fastball travel during that interval of no vision?

A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge. What is its speed when it reaches the valley beneath the bridge?

Draw two vector field diagrams, one for a particle carrying charge +q and located at the origin of a rectangular coordinate system and one for a particle carrying charge -2q and located at the origin. Describe the principal differences between the two diagrams.

The basal energy requirement for an individual indicates the minimum number of calories necessary to maintain essential life-sustaining processes such as circulation, regulation of body temperature, and respiration. Given a person's sex, weight $w$ (in kilograms), height $h$ (in centimeters), and age $y$ (in years), we can estimate the basal energy requirement in calories using the following formulas, where $C_f$ and $C_m$ are the calories necessary for females and males, respectively:

$$\begin{aligned} C_f &=66.5+13.8 w+5 h-6.8 y \\ C_m &=655+9.6 w+1.9 h-4.7 y \end{aligned}$$

(a) Determine the basal energy requirements first for a $25$-year-old female weighing $59$ kilograms who is $163$ centimeters tall and then for a $55$-year-old male weighing $75$ kilograms who is $178$ centimeters tall.

(b) Discuss why, in both formulas, the coefficient for $y$ is negative but the other coefficients are positive.

When you drive behind another car, what is the minimum distance you should keep between the cars to avoid a rear-end collision if the other car were to suddenly stop (it hits, say, a stationary truck)? Some drivers use a " $2$ second rule" while others use a "$3$ second rule." To apply such rules, pick out an object such as a tree alongside the road. When the front car passes it, begin to count off seconds. For the first rule, you want to pass that object at a count of $2 \mathrm{~s}$, and for the second rule, $3 \mathrm{~s}$. For the $2 \mathrm{~s}$ rule, what is the resulting car-car separation at a speed of $(a)$ $15.6 \mathrm{~m} / \mathrm{s}$ ($35 \mathrm{~m} / \mathrm{s}$), slow and $(b)$ $31.3 \mathrm{~m} / \mathrm{s}$ $(70 \mathrm{mi} / \mathrm{h}$), fast? For the $3 \mathrm{~s}$ rule, what is the car-car separation at a speed of $(c)$ $15.6 \mathrm{~m} / \mathrm{s}$ and $(d)$ $31.3 \mathrm{~m} / \mathrm{s}$ ? To check if the results give safe trailing distances, find the stopping distance required of you at those initial speeds. Assume that your car's braking acceleration is $-8.50 \mathrm{~m} / \mathrm{s}^2$ and your reaction time to apply the brake upon seeing the danger is $0.750 \mathrm{~s}$. What is your stopping distance at a speed of $(e)$ $15.6 \mathrm{~m} / \mathrm{s}$ and $(f)$ $31.3 \mathrm{~m} / \mathrm{s}$ ? $(g)$ For which is the $2 \mathrm{~s}$ rule adequate? $(h)$ For which is the $3 \mathrm{~s}$ rule adequate ?

In the start of a four-person bobsled race, two drivers (a pilot and a brakeman) are already on board while two pushers accelerate the sled along the ice by pushing against the ice with spiked shoes. After pushing for $50 \mathrm{~m}$ along a straight course, the pushers jump on board. The acceleration during the pushing largely determines the time to slide through the rest of the course and thus decides the winner with the least run time, which often depends on differences of $1.0 \mathrm{~ms}$. Consider an $x$ axis along the $50 \mathrm{~m}$, with the origin at the start position. If the position $x$ versus time $t$ in the pushing phase is given by $x=0.3305 t^2+4.2060 t$ (in meters and seconds), then at the end of a $9.000 \mathrm{~s}$ push what are $(a)$ the speed and $(b)$ the acceleration?

How much time would be required for a starship to reach Proxima Centauri, the star closest to the Sun, at a distance of $L=4.244$ light years(ly)? Assume that it starts from rest, maintains a comfortable acceleration magnitude of $1.000 \mathrm{~g}$ for the first $0.0450 \mathrm{~y}$ and a deceleration (slowing) magnitude of $1.000 \mathrm{~g}$ for the last $0.0450 \mathrm{~y}$, and cruises at constant speed in between those periods.

While driving a car at 90 km/h, how far do you move while your eyes shut for 0.50 s during a hard sneeze?

Which of the following is an example of discretionary fiscal policy? a. Income tax payments grow during an economic expansion. b. Congress spends an extra $2 billion to provide jobs for unemployed workers. c. Fewer workers receive unemployment compensation payments in an expansion. d. More people apply for and receive welfare benefits in a recession.

Muscles that help the skeleton move are

a. cardiac muscles

b. smooth muscles

c. skeletal muscles

d. involuntary muscles