Question: A vector A( has components Ax = -5.

> The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N east. If the boat (including its crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?

> A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true? (a) Its velocity and its acceleration are both zero. (b) Its velocity is not zero, but its acceleration is zero. (c) Its velocit

> An airplane in a holding pattern flies at constant altitude along a circular path of radius 3.50 km. If the airplane rounds half the circle in 1.50 x 102 s, determine the magnitude of its (a) Displacement (b) Average velocity during that time. (c) What i

> A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130. km in 2.00 h. (a) What is his total displacement? (b) What is his average velocity? Answer: (a) Displacement = &Delta

> A graph of position versus time for a certain particle moving along the x - axis is shown in Figure P2.6. Find the average velocity in the time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e) 0 to 8.00

> A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). (a) How long does the race take? (b) What is

> A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min rest stop. If the person’s average speed is 77.8 km/h, (a) How much time is spent on the trip and (b) How far does the person travel?

> A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true? (a) The car travels a distance υt. (b) The average speed of the car is υ/2

> A skydiver jumps out of a hovering helicopter. A few seconds later, another skydiver jumps out, so they both fall along the same vertical line relative to the helicopter. Assume both skydivers fall with the same acceleration. Does the vertical distance b

> The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 45 m in a straight line, reaching a final speed of 72 km/h. (a) Determine the cheetah’s average acceleration during the

> A ball is thrown straight up in the air. For which situation are both the instantaneous velocity and the acceleration zero? (a) On the way up (b) At the top of the flight path (c) On the way down (d) Halfway up and halfway down (e) None of these.

> A jet plane has a takeoff speed of υto = 75 m/s and can move along the runway at an average acceleration of 1.3 m/s2. If the length of the runway is 2.5 km, will the plane be able to use this runway safely? Defend your answer.

> Express the location of the fly in Problem 40 in polar coordinates. Data from Problem 40: A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.

> True or False? (a) A car must always have an acceleration in the same direction as its velocity. (b) It’s possible for a slowing car to have a positive acceleration. (c) An object with constant nonzero acceleration can never stop and remain at rest.

> Figure 2.4 shows the unusual path of a confused football player. After receiving a kickoff at his own goal, he runs downfield to within inches of a touchdown, then reverses direction and races back until he’s tackled at the exact locati

> A football player runs from his own goal line to the opposing team’s goal line, returning to the fifty-yard line, all in 18.0 s. Calculate (a) His average speed, and (b) The magnitude of his average velocity.

> Light travels at a speed of about 3 x 108 m/s. (a) How many miles does a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye? (b) Compare this distance to the diameter of Earth.

> An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x - direction, determine her average velocities symbolically in (a) The first half of the s

> Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far mu

> A tennis player moves in a straight-line path as shown in Figure P2.8. Find her average velocity in the time intervals from (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to 5.0 s.

> A ball is thrown vertically upward. (a) What are its velocity and acceleration when it reaches its maximum altitude? (b) What is the acceleration of the ball just before it hits the ground?

> Figure CQ2.6 shows strobe photographs taken of a disk moving from left to right under different conditions. The time interval between images is constant. Taking the direction to the right to be positive, describe the motion of the disk in each case. For

> Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negli

> (a) Can the equations in Table 2.4 be used in a situation where the acceleration varies with time? (b) Can they be used when the acceleration is zero?

> A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine

> If the velocity of a particle is zero, can the particle’s acceleration be nonzero? Explain.

> As the tennis ball of Quick Quiz 2.6 travels through the air, does its speed Data from Quick Quiz 2.6 A tennis player on serve tosses a ball straight up. While the ball is in free fall, does its acceleration (a) Increase (b) Decrease (c) Decrease and t

> The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain.

> The nearest neutron star (a collapsed star made primarily of neutrons) is about 3.00 x 1018 m away from Earth. Given that the Milky Way galaxy (Fig. P1.81) is roughly a disk of diameter, ~1021 m and thickness, ~ 1019 m, estimate the number of neutron sta

> An average person sneezes about three times per day. Estimate the worldwide number of sneezes happening in a time interval approximately equal to one sneeze.

> (a) How many Earths could fit inside the Sun? (b) How many of Earth’s Moons could fit inside the Earth?

> Assume there are 100 million passenger cars in the United States and that the average fuel consumption is 20 mi/gal of gasoline. If the average distance travelled by each car is 10,000 mi/yr, how much gasoline would be saved per year if average fuel cons

> A sphere of radius r has surface area A = 4πr2 and volume V = (4/3) πr3. If the radius of sphere 2 is double the radius of sphere 1, what is the ratio of (a) the areas, A2/A1 and (b) the volumes, V2 /V1

> One gallon of paint (volume = 3.79 x 10-3 m3) covers an area of 25.0 m2. What is the thickness of the fresh paint on the wall?

> Assume it takes 7.00 minutes to fill a 30.0-gal gasoline tank. (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in ho

> The displacement of an object moving under uniform acceleration is some function of time and the acceleration. Suppose we write this displacement as s = kamtn, where k is a dimensionless constant. Show by dimensional analysis that this expression is sati

> (a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be 55 mi/h. Use the conversion factor from part (a) to find the speed in kilometers per hour. (

> A tennis player on serve tosses a ball straight up. While the ball is in free fall, does its acceleration (a) Increase (b) Decrease (c) Increase and then decrease (d) Decrease and then increase, or (e) Remain constant?

> A commuter airplane starts from an airport and takes the route shown in Figure P1.71. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150. km 20.0° west of north, to city B

> The helicopter view in Figure P1.70 shows two people pulling on a stubborn mule. Find (a) The single force that is equivalent to the two forces shown and (b) The force a third person would have to exert on the mule to make the net force equal to zero. Th

> The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 41.0 km/h. Three hours later the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is t

> A map suggests that Atlanta is 730. miles in a direction 5.00° north of east from Dallas. The same map shows that Chicago is 560. miles in a direction 21.0° west of north from Atlanta. Figure P1.68 shows the location of these three

> A vector has an x - component of -25.0 units and a y - component of 40.0 units. Find the magnitude and direction of the vector.

> A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight downfield, perpendicular to the li

> A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her final position relative to her starting location? (b) What is the length of the path she walked?

> A figure skater glides along a circular path of radius 5.00 m. If she coasts around one half of the circle, find (a) Her distance from the starting location and (b) The length of the path she skated.

> The magnitude of vector A( is 35.0 units and points in the direction 325° counterclockwise from the positive x - axis. Calculate the x - and y - components of this vector.

> A person walks 25.0° north of east for 3.10 km. How far due north and how far due east would she have to walk to arrive at the same location?

> Figure 2.14a is a diagram of a multiflash image of an air puck moving to the right on a horizontal surface. The images sketched are separated by equal time intervals, and the first and last images show the puck at rest. (a) In Figure 2.14b, which color g

> Calculate (a) the x - component and (b) the y - component of the vector with magnitude 24.0 m and direction 56.0°.

> A roller coaster moves 2.00 x 102 ft horizontally and then rises 135 ft at an angle of 30.0° above the horizontal. Next, it travels 135 ft at an angle of 40.0° below the horizontal. Use graphical techniques to find the roller coaster’s displacement from

> A force F(1 of magnitude 6.00 units acts on an object at the origin in a direction θ = 30.0° above the positive x - axis (Fig. P1.58). A second force F(2 of magnitude 5.00 units acts on the object in the direction of the positive

> Vector A( is 3.00 units in length and points along the positive x - axis. Vector B( is 4.00 units in length and points along the negative y - axis. Use graphical methods to find the magnitude and direction of the vectors (a) A( + B( and (b) A( - B(

> An airplane flies 2.00 x 102 km due west from city A to city B and then 3.00 x 102 km in the direction of 30.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? (b) Relative to city A, in what direction i

> Vector A( has a magnitude of 29 units and points in the positive y - direction. When vector B( is added to A(, the resultant vector A( + B( points in the negative y - direction with a magnitude of 14 units. Find the magnitude and direction of B(.

> Vector A( has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x - axis. Vector B( also has a magnitude of 8.00 units and is directed along the negative x - axis. Using graphical methods, find (a) The vector sum A( + B( and (b) T

> A surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 x 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The ang

> A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.0°. Find the mountain’s height, neglecting the height of the woman’s eyes above the ground. Dra

> The three graphs in Figure 2.13 represent the position vs. time for objects moving along the x - axis. Which, if any, of these graphs is not physically possible?

> In Problem 50, what is the tangent of the angle for which 5.00 m is the opposite side? Data from Problem 50: In a certain right triangle, the two sides that are perpendicular to each other are 5.00 m and 7.00 m long.

> In a certain right triangle, the two sides that are perpendicular to each other are 5.00 m and 7.00 m long. What is the length of the third side of the triangle?

> In Figure P1.49, find (a) The side opposite θ (b) The side adjacent to ϕ (c) cos θ (d) sin ϕ and (e) tan ϕ.

> A right triangle has a hypotenuse of length 3.00 m, and one of its angles is 30.0°. What are the lengths of (a) The side opposite the 30.0° angle (b) The side adjacent to the 30.0° angle

> A high fountain of water is located at the center of a circular pool as shown in Figure P1.47. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 m. Next, the student stands at the edge of the pool

> A ladder 9.00 m long leans against the side of a building. If the ladder is inclined at an angle of 75.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

> For the triangle shown in Figure P1.45, what are (a) The length of the unknown side, (b) The tangent of θ, and (c) The sine of ϕ?

> Given points (r1, θ 1) and (r2, θ 2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as much as possible using the identity cos2 θ + sin2 θ = 1.

> Two points are given in polar coordinates by (r, θ) = (2.00 m, 50.0°) and (r, θ) = (5.00 m, -50.0°), respectively. What is the distance between them?

> Two points in a rectangular coordinate system have the coordinates (5.0, 3.0) and (23.0, 4.0), where the units are centimeters. Determine the distance between these points.

> Parts (a), (b), and (c) of Figure 2.10 represent three graphs of the velocities of different objects moving in straight - line paths as functions of time. The possible accelerations of each object as functions of time are shown in parts (d), (e), and (f)

> Your firm is contemplating the purchase of a new $535,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $30,000 at the end of that time. You will save $165,000 before tax

> In the previous problem, suppose the fixed asset actually qualifies for 100 percent bonus depreciation in the first year. What is the new NPV? Problem 14: Dog Up! Franks is looking at a new sausage system with an installed cost of $385,000. This cost wi

> Dog Up! Franks is looking at a new sausage system with an installed cost of $385,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for $60,000. The sausage s

> In the previous problem, suppose the fixed asset actually qualifies for 100 percent bonus depreciation in the first year. All the other facts are the same. What is the project’s Year 1 net cash flow now? Year 2? Year 3? What is the new NPV? Problem 12:

> In the previous problem, suppose the fixed asset actually falls into the three-year MACRS class. All the other facts are the same. What is the project’s Year 1 net cash flow now? Year 2? Year 3? What is the new NPV? Problem 11: In the previous problem,

> In the previous problem, suppose the project requires an initial investment in net working capital of $250,000, and the fixed asset will have a market value of $180,000 at the end of the project. What is the project’s Year 0 net cash flow? Year 1? Year 2

> In the previous problem, suppose the required return on the project is 12 percent. What is the project’s NPV? Problem 9: Esfandairi Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2.18 mi

> Parker & Stone, Inc., is looking at setting up a new manufacturing plant in South Park to produce garden tools. The company bought some land six years ago for $2.8 million in anticipation of using it as a warehouse and distribution site, but the company

> A project that provides annual cash flows of $15,300 for nine years costs $74,000 today. Is this a good project if the required return is 8 percent? What if it’s 20 percent? At what discount rate would you be indifferent between accepting the project and

> A firm evaluates all of its projects by applying the IRR rule. If the required return is 14 percent, should the firm accept the following project? Year ……………………… Cash Flow 0 ………………………….. −$41,000 1 ………………………………. 20,000 2 ………………………………. 23,000 3 ………………………

> You find a zero coupon bond with a par value of $10,000 and 24 years to maturity. If the yield to maturity on this bond is 4.2 percent, what is the dollar price of the bond? Assume semiannual compounding periods.

> You’re trying to determine whether to expand your business by building a new manufacturing plant. The plant has an installation cost of $12.6 million, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net

> Calculating Discounted Payback [LO3] An investment project costs $19,000 and has annual cash flows of $5,100 for six years. What is the discounted payback period if the discount rate is zero percent? What if the discount rate is 5 percent? If it is 19 pe

> An investment project has annual cash inflows of $2,800, $3,700, $5,100, and $4,300, for the next four years, respectively. The discount rate is 9 percent. What is the discounted payback period for these cash flows if the initial cost is $5,200? What if

> Kara, Inc., imposes a payback cutoff of three years for its international investment projects. If the company has the following two projects available, should it accept either of them?

> Anderson International Limited is evaluating a project in Erewhon. The project will create the following cash flows: Year ………………………………… Cash Flow 0 ………………………………… −$1,785,000 1 ………………………………………. 610,000 2 ………………………………………. 707,000 3 ………………………………………. 580,00

> Mako Corp. has a project with the following cash flows: Year ……………………………… Cash Flow 0 …………………………………… $25,000 1 …………………………….……… − 11,000 2 ………………………………………… 7,000 What is the IRR of the project? What is happening here?

> A project has the following cash flows: Year ……………………… Cash Flow 0 …………………………… $74,000 1 …………………………… − 49,000 2 …………………………… − 41,000 What is the IRR for this project? If the required return is 12 percent, should the firm accept the project? What is the

> The Yurdone Corporation wants to set up a private cemetery business. According to the CFO, Barry M. Deep, business is “looking up.” As a result, the cemetery project will provide a net cash inflow of $180,000 for the firm during the first year, and the c

> An investment under consideration has a payback of seven years and a cost of $745,000. If the required return is 11 percent, what is the worst-case NPV? The best-case NPV? Explain. Assume the cash flows are conventional.

> Suppose the company in the previous problem uses a discount rate of 11 percent and a reinvestment rate of 8 percent on all of its projects. Calculate the MIRR of the project using all three methods using these interest rates.

> Draiman Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $987. The bonds make semiannual payments. What must the coupon rate be on these bonds?

> An investment project provides cash inflows of $835 per year for eight years. What is the project payback period if the initial cost is $1,900? What if the initial cost is $3,600? What if it is $7,400?

> Duo Corp. is evaluating a project with the following cash flows: Year …………………………………………… Cash Flow 0 ………………………………………………. −$53,000 1 ……………………………………………………. 16,700 2 ……………………………………………………. 21,900 3 ……………………………………………………. 27,300 4 …………………………………………………... 20,400

> An investment has an installed cost of $574,380. The cash flows over the four-year life of the investment are projected to be $216,700, $259,300, $214,600, and $167,410, respectively. If the discount rate is zero, what is the NPV? If the discount rate is

> Consider the following two mutually exclusive projects: Whichever project you choose, if any, you require a return of 11 percent on your investment. a. If you apply the payback criterion, which investment will you choose? Why? b. If you apply the disco

> The Michner Corporation is trying to choose between the following two mutually exclusive design projects: a. If the required return is 10 percent and the company applies the profitability index decision rule, which project should the firm accept? b. If

> What is the profitability index for the following set of cash flows if the relevant discount rate is 10 percent? What if the discount rate is 15 percent? If it is 22 percent? Year ………………………………….. Cash Flow 0 ………………………………………. −$14,800 1 …………………………………….……

> Howell Petroleum, Inc., is trying to evaluate a generation project with the following cash flows: Year ……………………… Cash Flow 0 ………………….. −$52,000,000 1 ………………………. 74,000,000 2 …………………… − 12,000,000 a. If the company requires a return of 12 percent on its

> Consider the following two mutually exclusive projects: Sketch the NPV profiles for X and Y over a range of discount rates from zero to 25 percent. What is the crossover rate for these two projects?