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.

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?

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?

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 basketball player grabbing a rebound jumps $76.0\text{~ cm}$ vertically. How much total time (ascent and descent) does the player spend in the top $15.0 \text{~cm}$ of this jump ? (The player seems to hang in the air at the top.)

Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in rods? (1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.)

One common form of aggressive driving is for a trailing driver to repeat a pattern of accelerating suddenly to come close to the car in front and then braking suddenly to avoid a collision. One way to monitor such behavior, either remotely or with an onboard computer system, is to measure vehicle jerk, where jerk is the physics term for the time rate of change of an object's acceleration along a straight path. Figure $2.38$ is a graph of acceleration $a$ versus time $t$ in a typical situation for a car. Determine the jerk for each of the time periods: (a) gas pedal pushed down rapidly, $2.0 \mathrm{~s}$ interval, (b) gas pedal released, $1.5 \mathrm{~s}$ interval, (c) brake pedal pushed down rapidly, $1.5 \mathrm{~s}$ interval, (d) brake pedal released, $2.5 \mathrm{~s}$ interval.

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 mi/h, slow) and (b) $31.3 \mathrm{~m} / \mathrm{s}(70 \mathrm{mi} / \mathrm{h}$, fast)? For the 3 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?

Receivables are

a. One of the most liquid assets and thus are always considered current assets

b. Claims that are expected to be collected in cash

c. Shown on the Income Statement at cash realizable value

d. Always the result of revenue recognition

Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate dV/dx when x = 3 mm and explain its meaning.

Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function T = 0.02t + 8.50, where T is temperature in °C and t represents years since 1900. What do the slope and T-intercept represent?