Question: Figure 1.7 shows the result of
Figure 1.7 shows the result of an unacceptable error in the stopping position of a train. If a train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10.0 m, what is the percent error in the total distance covered? Is it correct to write the total distance covered by the train as 890,010 m? Explain. Figure 1.7: 
Transcribed Image Text:
Scalar (dot) product of vectors A and B Components of Å А - В %3D А, В, + A, В, + A,B, (1.19) Components of B
> A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle’s position as a function of time is x (t) = 50.0 cm +(2.00 cm>s) t –(0.0625 cm/s2)t2. (a) Find the turtle’s initial
> Under what conditions does the magnitude of the average velocity equal the average speed?
> A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car’s motion, the eastward component of the car’s velocity is given by vx(t)=(0.860 m>s3)t2. What is the acceleration of the car when vx = 12.0 m/s?
> The table shows test data for the Bugatti Veyron Super Sport, the fastest street car made. The car is moving in a straight line (the x-axis). (a) Sketch a vx-t graph of this car’s velocity (in mi/h) as a function of time. Is its accel
> Figure E2.12 shows the velocity of a solar-powered car as a function of time. The driver accelerates from a stop sign, cruises for 20 s at a constant speed of 60 km / h, and then brakes to come to a stop 40 s after leaving the stop sign. (a) Compute the
> A test car travels in a straight line along the x-axis. The graph in Fig. E2.11 shows the car’s position x as a function of time. Find its instantaneous velocity at points A through G. Fig. E2.11: Figure E2.11 x (m) 40 30 FA 20 10
> A physics professor leaves her house and walks along the sidewalk toward campus. After 5 min it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.10. At which of the labeled points is her velocity
> High-speed motion pictures (3500 frames>second) of a jumping, 210-mg flea yielded the data used to plot the graph in Fig. E2.54. (See “The Flying Leap of the Flea” by M. Rothschild, Y. Schlein, K. Parker, C. Neville
> The acceleration of a motorcycle is given by ax(t)= At - Bt2, where A = 1.50 m/s3 and B = 0.120 m/s4. The motorcycle is at rest at the origin at time t = 0. (a) Find its position and velocity as functions of time. (b) Calculate the maximum velocity it at
> The acceleration of a bus is given by ax(t)= at, where a = 1.2 m/s3. (a) If the bus’s velocity at time t = 1.0 s is 5.0 m/s, what is its velocity at time t = 2.0 s ? (b) If the bus’s position at time t = 1.0 s is 6.0 m, what is its position at time t = 2
> A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay =(2.80 m/s3)t, where the +y-direction is upward. (a) What is the height of the rocket abo
> A small object moves along the x-axis with acceleration ax(t)= -(0.0320 m/s3)(15.0 s – t). At t = 0 the object is at x = -14.0 m and has velocity v0x = 8.00 m/s. What is the x-coordinate of the object when t = 10.0 s?
> Is it possible for an object to be (a) slowing down while its acceleration is increasing in magnitude; (b) speeding up while its acceleration is decreasing? In both cases, explain your reasoning.
> You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, 6.00 s after it was thrown. What is the speed of the rock just before it reaches the water 28.0 m below the point where the ro
> For the two vectors
> For the two vectors A and D in Fig. E1.24, find the magnitude and direction of (a) the vector product
> For the two vectors in Fig. E1.35, find the magnitude and direction of (a)the vector product
> Find the angle between each of these pairs of vectors: (a)
> Find the vector product
> For tℎe vectors
> (a) Find the scalar product of the vectors
> Given two vectors
> You are given two vectors
> The U.S. National Institute of Standards and Technology (NIST) maintains several accurate copies of the international standard kilogram. Even after careful cleaning, these national standard kilograms are gaining mass at an average rate of about 1 mg>y (y
> (a) Write each vector in Fig. E1.39 in terms of the unit vectors
> Given two vectors
> Write each vector in Fig. E1.24 in terms of the unit vectors
> A small rock is thrown vertically upward with a speed of 22.0 m/s from the edge of the roof of a 30.0-m-tall building. The rock doesn’t hit the building on its way back down and lands on the street below. Ignore air resistance. (a) What is the speed of t
> Vector
> Find the magnitude and direction of the vector represented by the following pairs of components: (a) Ax = -8.60 cm, Ay = 5.20 cm; (b) Ax = -9.70 m, Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km.
> A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an area of 43,600 ft2. If a lot has an area of 12.0 acres, what is its area in hectares?
> The density of gold is 19.3 g/cm3. What is this value in kilograms per cubic meter?
> In each case, find the x- and y-components of vector
> Vector
> Vector
> In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 km away, and released. The bird found its way back to its nest 13.5 days after release. If we place the origin at the nest and extend the +x-axis to the release point, what wa
> A car travels in the +x-direction on a straight and level road. For the first 4.00 s of its motion, the average velocity of the car is vav-x = 6.25 m/s. How far does the car travel in 4.00 s?
> A projectile is fired upward at an angle u above the horizontal with an initial speed v0. At its maximum height, what are its velocity vector, its speed, and its acceleration vector?
> If a jumping frog can give itself the same initial speed regardless of the direction in which it jumps (forward or straight up), how is the maximum vertical height to which it can jump related to its maximum horizontal range R max = v 2 0>g?
> At the instant that you fire a bullet horizontally from a rifle, you drop a bullet from the height of the gun barrel. If there is no air resistance, which bullet hits the level ground first? Explain.
> In a rainstorm with a strong wind, what determines the best position in which to hold an umbrella?
> In uniform circular motion, the acceleration is perpendicular to the velocity at every instant. Is this true when the motion is not uniform—that is, when the speed is not constant?
> In uniform circular motion, how does the acceleration change when the speed is increased by a factor of 3? When the radius is decreased by a factor of 2?
> If = 0 for a vector in the xy-plane, does it follow that Ax = -Ay? What can you say about Ax and Ay?
> (a) If A ⃗ . B ⃗ = 0, does it necessarily follow that A = 0 or B = 0? Explain. (b) If A ⃗ × B ⃗ = 0, does it necessarily follow that A = 0 or B = 0? Explain.
> Show that, no matter what
> Consider the vector products
> When a Dodge Viper is at Elwood’s Car Wash, a BMW Z3 is at Elm and Main. Later, when the Dodge reaches Elm and Main, the BMW reaches Elwood’s Car Wash. How are the cars’ average velocities between these two times related?
> Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with x0 = y0 = 0 and 0 6 a0 6 90°.
> Let represent any nonzero vector. Why is / A a unit vector, and what is its direction? If u is the angle that makes with the +x-axis, explain why ( A ⃗ / A)* is called the direction cosine for that axis. Q1.21 Fi
> What does
> If A ⃗ and B ⃗ are nonzero vectors, is it possible for both A ⃗ . B ⃗ and A ⃗ × B ⃗ to be zero? Explain.
> If C ⃗ = A ⃗ + B ⃗, what must be true about the directions and magnitudes of A ⃗ and B ⃗ if C = A + B? What must be true about the directions and magnitudes of A ⃗ and B ⃗ if C = 0?
> Under constant acceleration the average velocity of a particle is half the sum of its initial and final velocities. Is this still true if the acceleration is not constant? Explain.
> Can you find a vector quantity that has a magnitude of zero but components that are not zero? Explain. Can the magnitude of a vector be less than the magnitude of any of its components? Explain.
> Air traffic controllers give instructions called “vectors” to tell airline pilots in which direction they are to fly. If these are the only instructions given, is the name “vector” used correctly? Why or why not?
> The “direction of time” is said to proceed from past to future. Does this mean that time is a vector quantity? Explain.
> An automobile is traveling west. Can it have a velocity toward the west and at the same time have an acceleration toward the east? Under what circumstances?
> A package falls out of an airplane that is flying in a straight line at a constant altitude and speed. If you ignore air resistance, what would be the path of the package as observed by the pilot? As observed by a person on the ground?
> A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track? Explain.
> Is the vector (
> Three archers each fire four arrows at a target. Joe’s four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm from the center, a
> What are the units of volume? Suppose another student tells you that a cylinder of radius r and height h has volume given by pr3h. Explain why this cannot be right.
> The quantity p = 3.14159c is a number with no dimensions, since it is a ratio of two lengths. Describe two or three other geometrical or physical quantities that are dimensionless.
> Describe how you could measure the thickness of a sheet of paper with an ordinary ruler.
> What physical phenomena (other than a pendulum or cesium clock) could you use to define a time standard?
> Under what conditions is average velocity equal to instantaneous velocity?
> A projectile moves in a parabolic path without air resistance. Is there any point at which
> Suppose you are asked to compute the tangent of 5.00 meters. Is this possible? Why or why not?
> A book slides off a horizontal tabletop. As it leaves the table’s edge, the book has a horizontal velocity of magnitude v0. The book strikes the floor in time t. If the initial velocity of the book is doubled to 2v0, what happens to (a) the time the book
> What is your height in centimeters? What is your weight in newtons?
> Does the speedometer of a car measure speed or velocity? Explain.
> Each of the values of h and R has some measurement error: The muzzle speed is not precisely the same each time, and the barrel isn’t precisely horizontal. So you use all of the measurements to get the best estimate of v0. No wind is blowing, so you decid
> You have constructed a hair-spray-powered potato gun and want to find the muzzle speed v0 of the potatoes, the speed they have as they leave the end of the gun barrel. You use the same amount of hair spray each time you fire the gun, and you have confirm
> A spring-gun projects a small rock from the ground with speed v0 at an angle u0 above the ground. You have been asked to determine v0. From the way the spring-gun is constructed, you know that to a good approximation v0 is independent of the launch angle
> Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m>s. The velocity of the ball relative to Mia is 5.00 m/s in a direction 30.0o east of south. What are the magnitude and directi
> An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to the elevator floor? What is the speed of the bolt just a
> In a World Cup soccer match, Juan is running due north toward the goal with a speed of 8.00 m/s relative to the ground. A teammate passes the ball to him. The ball has a speed of 12.0 m/s and is moving in a direction 37.0° east of north, relative to the
> When a train’s velocity is 12.0 m/s eastward, raindrops that are falling vertically with respect to the earth make traces that are inclined 30.0° to the vertical on the windows of the train. (a) What is the horizontal component of a drop’s velocity with
> An airplane pilot sets a compass course due west and maintains an airspeed of 220 km/h. After flying for 0.500 h, she finds herself over a town 120 km west and 20 km south of her starting point. (a) Find the wind velocity (magnitude and direction). (b) I
> A student sits atop a platform a distance h above the ground. He throws a large firecracker horizontally with a speed v. However, a wind blowing parallel to the ground gives the firecracker a constant horizontal acceleration with magnitude a. As a result
> Redraw Fig. 3.11a if
> In the middle of the night you are standing a horizontal distance of 14.0 m from the high fence that surrounds the estate of your rich uncle. The top of the fence is 5.00 m above the ground. You have taped an important message to a rock that you want to
> A firefighting crew uses a water cannon that shoots water at 25.0 m/s at a fixed angle of 53.0° above the horizontal. The firefighters want to direct the water at a blaze that is 10.0 m above ground level. How far from the building should they position t
> A cart carrying a vertical missile launcher moves horizontally at a constant velocity of 30.0 m/s to the right. It launches a rocket vertically upward. The missile has an initial vertical velocity of 40.0 m/s relative to the cart. (a) How high does the r
> Henrietta is jogging on the sidewalk at 3.05 m/s on the way to her physics class. Bruce realizes that she forgot her bag of bagels, so he runs to the window, which is 38.0 m above the street level and directly above the sidewalk, to throw the bag to her.
> A 76.0-kg rock is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake (Fig. P3.65). The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface
> A 2.7-kg ball is thrown upward with an initial speed of 20.0 m>s from the edge of a 45.0-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straig
> A 2.7-kg ball is thrown upward with an initial speed of 20.0 m>s from the edge of a 45.0-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straig
> A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig. P3.63). The takeoff ramp was inclined at 53.0°, the river was 40.0 m wide, and the far bank was 15.0 m lower
> A rock is thrown with a velocity v0, at an angle of a0 from the horizontal, from the roof of a building of height h. Ignore air resistance. Calculate the speed of the rock just before it strikes the ground, and show that this speed is independent of a0.
> Suppose that the boy in Problem 3.60 throws the ball upward at 60.0° above the horizontal, but all else is the same. Repeat parts (a) and (b) of that problem. Data from Problem 3.60: A boy 12.0 m above the ground in a tree throws a ball for his dog, wh
> A stone is thrown into the air at an angle above the horizontal and feels negligible air resistance. Which graph in Fig. Q3.16 best depicts the stone’s speed v as a function of time t while it is in the air? Fig. Q3.16: (a) (b) (c
> A boy 12.0 m above the ground in a tree throws a ball for his dog, who is standing right below the tree and starts running the instant the ball is thrown. If the boy throws the ball horizontally at 8.50 m/s, (a) how fast must the dog run to catch the bal
> A snowball rolls off a barn roof that slopes downward at an angle of 40° (Fig. P3.59). The edge of the roof is 14.0 m above the ground, and the snowball has a speed of 7.00 m>s as it rolls off the roof. Ignore air resistance. (a) How far fr
> In Canadian football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. The bar is 10.0 ft above the ground, and the ball is kicked from ground level, 36.0 ft horizontally from
> A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.57. Find (a) the initial speed of the grasshopper and (b) the height of the cliff. Fig. P3.57: Figure P3.57 6.74 cm 50.0° Not to scale 1.06 m
> A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D. The hose shoots the water at 45° above the horizontal from the same level as the base of the tank and is a distance 6D away (Fig. P3.56). For what range
> A baseball thrown at an angle of 60.0° above the horizontal strikes a building 18.0 m away at a point 8.00 m above the point from which it is thrown. Ignore air resistance. (a) Find the magnitude of the ball’s initial velocity (the velocity with which th
> An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150 m above the level ground when the plane is flying at 75 m/s in a direction 55° above the horizontal. How far in front of the ca
