Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
From New York to Miami Again The city of Richmond, Virginia, is about halfway between New York and Miami. A Richmond resident might locate the airplane in Example 6.1 using distance north of Richmond. Make the graphs of location and velocity of the airplane from this perspective.
EXAMPLE 6.1 FROM NEW YORK TO MIAMI
An airplane leaves Kennedy Airport in New York and flies to Miami, where it is serviced and receives new passengers before returning to New York. Assume that the trip is uneventful and that after each takeoff, the airplane accelerates to its standard cruising speed, which it maintains until it decelerates prior to landing.
Part 1 Describe what the graph of distance south of New York looks like during the period when the airplane is maintaining its standard cruising speed on the way to Miami.
Part 2 Say we locate the airplane in terms of its distance south of New York. Make possible graphs of its distance south of New York versus time and of the velocity of the airplane versus time.
Part 3 Say we locate the airplane in terms of its distance north of Miami. Make possible graphs of its distance north of Miami versus time and of the velocity of the airplane versus time.
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Walking and Running You live east of campus, and you are walking from campus toward your home at a constant speed. When you get there, you rest for 5minutes and then run back west at a rapid speed. After a few minutes, you reach your destination, and then you rest for 10minutes. Measure your location as your distance west of your home, and make graphs of your location and velocity.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The Rock with a Changed Reference Point Make graphs of position and velocity for a rock tossed upward from ground level as it might be viewed by someone standing atop a tall building. Thus, the location of the rock is measured by its distance down from the top of the building.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Rubber Ball A rubber ball is dropped from the top of a building. The ball lands on concrete and bounces once before coming to rest on the grass. Measure the location of the ball as its distance up from the ground. Make graphs of the location and velocity of the ball.arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. InflationDuring a period of high inflation, a political leader was up for re-election. Inflation had been increasing during his administration, but he announced that the rate of increase of inflation was decreasing. Draw a graph of inflation versus time that illustrates this situation. Would this announcement convince you that economic conditions were improving?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Gravity on Earth and on MarsThe acceleration due to gravity near the surface of a planet depends on the mass of the planet; larger planets impart greater acceleration than smaller ones. Mars is much smaller than Earth. A rock is dropped from the top of a cliff on each planet. Give its location as the distance down from the top of the cliff. a.On the same coordinate axes, make a graph of distance down for each of the rocks. b.On the same coordinate axes, make a graph of velocity for each of the rocks.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. The Cannon with a Different Muzzle VelocityIf the cannonball from example 6.7 is fired with a muzzle velocity of 370feetpersecond, it will follow the graph of h=x32(x370)2, where distances are measured in feet. a.Plot the graph of the flight of the cannonball. b.Find the height of the cannonball 3000feet downrange. c.By looking at the graph of h, determine whether dhdx is positive or negative at 3000feet downrange. d.Calculate dhdx at 3000feet downrange and explain what this number means in practical terms.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. TravelIng in a CarMake graphs of location and velocity for each of the following driving events. In each case, assume that the car leaves from home moving west down a straight road and that position is given as the distance west from home. a. A vacation: Being eager to begin your overdue vacation, you set your cruise control and drive faster than you should to the airport. You park your car there and get on an airplane to Spain. When you fly back 2 weeks later, you are tired, and you drive back home at a leisurely pace. Note: Here we are talking about the location of your car, not of the airplane. b. On a country road: A car driving down a country road encounters a deer. The driver slams on the brakes, and the deer runs away. The journey is cautiously resumed. c. At the movies: In a movie chase scene, our hero is driving his car rapidly toward the bad guys. When the danger is spotted, he does a Hollywood 180-degree turn and speeds off in the opposite direction.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The Rock with a Formula If from ground level we toss a rock upward with a velocity of 30feetpersecond, we can use elementary physics to show that the height in feet of the rock above the ground t seconds after the toss is given by S=30t16t2. a. Use your calculator to plot the graph of S versus t. b. How high does the rock go? c. When does it strike the ground? d. Sketch the graph of the velocity of the rock versus time.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Making Up a Story about a Car TripYou begin from home on a car trip. Initially your velocity is a small positive number. Shortly after you leave, your velocity decreases momentarily to zero. Then it increases rapidly to a large positive number and remains constant for this part of the trip. After a time, your velocity decreases to zero and then changes to a large negativc number. a. Make a graph of velocity for this trip. b. Discuss your distance from home during this driving event, and make a graph. c. Make up a driving story that matches this description.arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. Falling with a parachuteWhen an average-sized man with a parachute jumps from an airplane, he will fall S=12.5(0.2t1)+20t feet in t seconds. a.Plot the graph of S versus t over at least the first 10seconds of the fall. b.How far does the parachutist fall in 2seconds? c.Calculate dSdt at 2seconds into the fall and explain what the number you calculated means in practical terms.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Wind ChillThe graph in Figure 1.40 shows the temperature T = Tv adjusted for wind chill as a function of the velocity v of the wind when the thermometer reads 30 degrees Fahrenheit. The adjusted temperature T shows the temperature that has an equivalent cooling power when there is no wind. a. At what wind speed is the temperature adjusted for wind chill equal to 0? b. Your answer in part a is the solution of an equation involving Tv. Which equation? c. At what value of v would a small increase in v have the greatest effect on Tv? In other words, at what wind speed could you expect a small increase in wind speed to cause the greatest change in wind chill? Explain your reasoning. d. Suppose the wind speed is 45 miles per hour. Judging from the shape of the graph, how significant would you expect the effect on Tv to be if the wind speed increased? FIGURE 1.40 Temperature adjusted for wind chill when the thermometer reads 30 degrees Fahrenheit.arrow_forwardReminder Round all answers to decimal places unless otherwise indicated. Health Plan The managers of an employee health plan for a firm have studied the balance B, in millions of dollars, in the plan account as a function of t, the number of years since the plan was instituted. They have determined that the rate of change dBdt in the account balance is given by the formula dBdt=10e0.1t12. a. Use your calculator to make a graph of dBdt versus t over the first 5 years of the plan. b. During what period is the account balance B decreasing? c. At what time is the account balance B at its minimum?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning