Question: For the two vectors A and D

> All of the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. Figure P1.91 shows the distances from the earth to each of these stars. The distan

> The football team at Enormous State University (ESU) uses vector displacements to record its plays, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at +1.0

> Can you have zero displacement and nonzero average velocity? Zero displacement and nonzero velocity? Illustrate your answers on an x-t graph.

> A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 1.00 s later. Ignore air resistance. (a) If the height of the building is 20.0 m, what must the initial speed of the first ball be if both are to

> A student is running at her top speed of 5.0 m/s to catch a bus, which is stopped at the bus stop. When the student is still 40.0 m from the bus, it starts to pull away, moving with a constant acceleration of 0.170 m/s2. (a) For how much time and what di

> In the vertical jump, an athlete starts from a crouch and jumps upward as high as possible. Even the best athletes spend little more than 1.00 s in the air (their “hang time”). Treat the athlete as a particle and let ymax be his maximum height above the

> A 7500-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25 m/s2 and feels no appreciable air resistance. When it has reached a height of 525 m, its engines suddenly fail; the only force acting on it is now grav

> A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.90 s. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is the building? (b) What is the magnitude of the brick’s v

> A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. When you see the meter stick released, you grab it with those two fingers. You can calculate your reaction time from the distance the meter stick fa

> A lunar lander is making its descent to Moon Base I (Fig. E2.40). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is 5.0 m above the surface and has a downward speed of 0.8 m/s. With the engi

> A tennis ball on Mars, where the acceleration due to gravity is 0.379g and air resistance is negligible, is hit directly upward and returns to the same level 8.5 s later. (a) How high above its original point did the ball go? (b) How fast was it moving j

> A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the

> Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 60 minutes, reaching a point 2.0 km farther upstream. At this point they realize that the bottle is missing an

> A driver in Massachusetts was sent to traffic court for speeding. The evidence against the driver was that a policewoman observed the driver’s car alongside a second car at a certain moment, and the policewoman had already clocked the second car going fa

> A projectile thrown from a point P moves in such a way that its distance from P is always increasing. Find the maximum angle above the horizontal with which the projectile could have been thrown. Ignore air resistance.

> At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 2.80 m/s2. At the same instant a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car. (

> A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled 6.80 m to the bottom of the incline is 3.80 m/s. What is the speed of the blo

> Two cars, A and B, move along the x-axis. Figure E2.32 is a graph of the positions of A and B versus time. (a) In motion diagrams (like Figs. 2.13b and 2.14b), show the position, velocity, and acceleration of each of the two cars at t = 0, t = 1 s, and t

> The graph in Fig. E2.31 shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at t = 3 s, t = 7 s, and t = 11 s. (b) How far does the officer go in the first 5 s? The first 9 s? The first

> You normally drive on the freeway between San Diego and Los Angeles at an average speed of 105 km/h 165 mi/h2, and the trip takes 1 h and 50 min. On a Friday afternoon, however, heavy traffic slows you down and you drive the same distance at an average s

> A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 20 m/s 145

> It has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a meteor hit Mars and blasted pieces of rock (perhaps containing primitive life) free of the Martian surface. Astronomers know that man

> Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip’s speed at impact is about 2.0 m/s. If this can be reduced to 1.3 m/s or less, the hip will usually not fracture. One way to do this is by wear

> During an auto accident, the vehicle’s air bags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, air bags produce a maximum acceleration of 60g that lasts for only 36 ms

> Can an object with constant acceleration reverse its direction of travel? Can it reverse its direction twice? In both cases, explain your reasoning.

> A pilot who accelerates at more than 4g begins to “gray out” but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of so

> The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2. If you are in an automobile accident with an initial speed of 105 km/h 165 mi/h2 and are stopped by an airbag that inflat

> In the fastest measured tennis serve, the ball left the racquet at 73.14 m/s. A served tennis ball is typically in contact with the racquet for 30.0 ms and starts from rest. Assume constant acceleration. (a) What was the ball’s acceleration during this s

> The fastest measured pitched baseball left the pitcher’s hand at a speed of 45.0 m/s. If the pitcher was in contact with the ball over a distance of 1.50 m and produced constant acceleration, (a) what acceleration did he give the ball, and (b) how much t

> A jet fighter pilot wishes to accelerate from rest at a constant acceleration of 5g to reach Mach 3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will black out if this acceleration lasts for more than 5.0 s.

> An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 6.00 s. Its speed as it passes the second point is 15.0 m/s. What are (a) its speed at the first point and (b) its acceleration?

> The position of the front bumper of a test car under microprocessor control is given by x (t)= 2.17 m + (4.80 m/s2)t2 –(0.100 m/s6)t6. (a) Find its position and acceleration at the instants when the car has zero velocity. (b) Draw x-t, vx-t, and ax-t gra

> A car’s velocity as a function of time is given by vx(t)= a + bt2, where a = 3.00 m/s and b = 0.100 m/s3. (a) Calculate the average acceleration for the time interval t = 0 to t = 5.00 s. (b) Calculate the instantaneous acceleration for t = 0 and t = 5.0

> An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 10-s interval. What are the magnitude, the algebraic sign, and the direction of the average acc

> 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 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°.

> 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 co

> 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?