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physics
mechanics

Questions and Answers of Mechanics

The two vectors A and B are drawn from a common point, and C = 1 + B. (a) Show that if C2 = A2 + B2, the angle between the vectors A and B is 90°. (b) Show that if C2 < A2 + B2, the angle
When two vectors 1 and B are drawn from a common point, the angle between them is Φ.(a) Using vector techniques. Show that the magnitude of their vector sum is given by √ A2 + B2 + 2ABcosΦ(b) If
If A and B have the same magnitude, for which value of Φ will their vector sum have the same magnitude as 1 or B?
A cube is placed so that one comer is at the origin and three edges are along the x-, y-, and z-axes of a coordinate system (Fig. 1.43). Use vectors to compute(a) The angle between the edge along the
Obtain a unit vector perpendicular to the two vectors given in Problem 1.89.
You are given vectors 1 = 5i - 6.5J and B = -3.5i + 7.0j. A third vector C lies in the xy-plane. Vector C is perpendicular to vector 1, and the scalar product of C with B is 15.0. From this
Two vectors 1 and B have magnitude A = 3.00 and B = 3.00. Their vector product is A X B = -5.00k + 2.00i.What is the angle between A and B?
Later in our study of physics we will encounter quantities represented by (A X 11) • C. (a) Prove that for any three vectors A, B, and C, A• (B X c) = (A X B) • C. (b) Calculate (A X B) • C
The length of a rectangle is given as L ± I and its with as W ± w.(a) Show that the uncertainty in its area A is a = Lw + lW. Assume that the uncertainties I and w are small. so that the product lw
Completed pass at Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a
Navigating in the Big Dipper All 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.
The vector r = xl + yj + zk, called the position vector, points from the origin (0. 0, o) to an arbitrary point in space with coordinates (x, y, z). Use what you know about vectors to prove the
Starting with the definition I in. = 2.54 cm, find the number of (a) Kilometers in 1.00 mile and (b) Feet in 1.00 km.
A rocket carrying a satellite is accelerating straight up from the earth's surface. At 1.15 s after liftoff, the rocket clears the top of its launch platform, 63 m above the ground. After an
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 in the
Trip Home you normally drive on the freeway between San Diego and Los Angeles at an average speed of 105 km/h (65 mi/h), and the trip takes 2 h and 20 min. On a Friday afternoon, however, heavy
From Pillar to Post Starting from a pillar, you run 200 m east (the + x-direction) at an average speed of 5.0 m/s, and then run 280 m west at an average speed of 4.0 m/s to a post. Calculate (a)
Two runners start simultaneously from the same point on a circular 200-m track and run in opposite directions. One runs at a constant speed of 6.20 m/s, and the other runs at a constant speed of 5.50
Suppose the two runners in Exercise 2.5 start at the same time from the same place but run in the same direction. (a) When will the fast one first overtake ("lap") the slower one, and how far from
Earthquake Analysis Earthquakes produce several types of shock waves_ The most well known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust,
A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x (t} = at2 - pt', where a = 1.50m/S2 and p = 0.0500 m/s'.
A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x (t) = bt2 - ct', where b = 2.40m/S2 and c = O.I20m/s'. (a) Calculate the
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.
A ball moves in a straight line (the x-axis). The graph in Fig. 2.33 shows this ball's velocity as a function of time.(a) What are the ball's average speed and average velocity during the first 3.0
A test driver at Incredible Motors, Inc., is testing a new model car with a speedometer calibrated to read m/s rather than mi/h. The following series of speedometer readings was obtained during a
The Fastest (and Most Expensive) Car! The table shows test data for the Bugatti Veyron, the fastest car made. The car is moving in a straight line (the x-axis).(a) Make a v.-t graph of this car's
Figure 2.34 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
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) = SO.O cm + (2.00
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,
Auto Acceleration Based on your experiences of riding in automobiles, estimate the magnitude of a car's average acceleration when it (a) Accelerates onto a freeway from rest to 65 mi/h, and (b)
A car's velocity as a function of time is given by vx, (t) = a + Bt2, where a = 3.00 m/s and p = 0.100 m/s3. (a) Calculate the average acceleration for the time interval, = 0 to, = 5.00 s. (b)
Figure 2.35 is a graph of the coordinate of a spider crawling along the x-axis. (a) Graph its velocity and acceleration as functions of time. (b) In a motion diagram (like Fig. 2.13b and 2.14b),
The position of the front bumper of a test car under microprocessor control is given by x (t) = 2.17m + (4.80m/S2) t2 - (0.100 m/S6) t6• (a) Find its position and acceleration at the instants
An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 7.00 s. Its speed as it passes the second point is 15.0 m/s. (a) What is its speed at the first
The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A-18 Hornet jet fighter from rest to a takeoff speed of 173 mi/h in a distance of 307 ft. Assume constant acceleration. (a)
A Fast Pitch 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
A Tennis Serve 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
Automobile Airbags 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
Entering the Freeway a car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver accelerates with constant acceleration along the ramp and onto the freeway. The car
Launch of the Space Shuttle at launch the space shuttle weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h, and at the end of the first 1.00 min its speed is
According to recent test data, an automobile travels 0.250 mi in 19.9 s, starting from rest. The same car, when braking from 60.0 mi/h on dry pavement, stops in 146 ft. Assume constant acceleration
A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of
At t = 0 a car is stopped at a traffic light. When the light toms green, the car starts to speed up, and gains speed at a constant rate until it reaches a speed of 20 m/s 8 seconds after the light
The graph in Figure shows the velocity of a motorcycle police officer plotted as a function of time.(a) Find the instantaneous acceleration at t = 3 s, at t = 7 s, and at t = 11 s.(b) How far does
Figure 2.38 is a graph of the acceleration of a model railroad locomotive moving on the x-axis. Graph its velocity and x coordinate as functions of time if x = 0 and v. = 0 at t = o.
A spaceship ferrying workers to Moon Base I takes a straight-line path from the earth to the moon, a distance of 384,000 km. Suppose the spaceship starts from rest and accelerates at 20.0 m/s2 for
A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s2 for 14.0 s. It runs at constant speed for 70.0 s and slows down at a rate of 3.50 m/s2 until it stops at the next
Two cars, A and B, move along the x-axis. Figure 2.39 is a graph of the positions of A 25 x (m) and B versus time. (a) In motion diagrams (like Figs. 2.13b and 2.14b), show the position, velocity,
At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/S2. At the same instant a truck, traveling with a
Mars Landing In January 2004, NASA landed exploration vehicles on Mars. Part of the descent consisted of the following stages: Stage A: Friction with the atmosphere reduced the speed from 19,300
Raindrops if the effects of the air acting on falling raindrops are ignored, then we can treat raindrops as freely falling objects. (a) Rain clouds are typically a few hundred meters above the
(a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? (b) How long is it in the air?
Touchdown on the Moon a lunar lander is making its descent to Moon Base I (Fig. 2.40). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander
A Simple Reaction-Time Test A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. On seeing the meter stick released, you grab it with these two
A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 2.50 s. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is
Launch Failure. 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
A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 m/s, releases a sandbag at an instant when the balloon is 40.0 m above the ground (Fig. 2.41). After it is released,
A student throws a water balloon vertically downward from the top of a building. The balloon leaves the thrower's hand with a speed of 6.00 m/s. Air resistance may be ignored, so the water balloon is
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point 50.0 m below its starting point 5.00 s after
The rocket-driven sled Sonic Wind No.2, used for investigating the physiological effects of large accelerations, runs on a straight, level track 1070 m (3500 ft) long. Starting from rest, it can
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Air resistance may be ignored.(a) At what time after being ejected is the boulder moving at 20.0 m/s
A 15-kg rock is dropped from rest on the earth and reaches the ground in 1.75 s. When it is dropped from the same height on Saturn's satellite Enceladus, it reaches the ground in 18.6 s. What is the
The acceleration of a bus is given by a. (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
The acceleration of a motorcycle is given by a. (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 = O. (a) Find its position and velocity as
Flying Leap of the Flea High-peed motion pictures (3500 frames/second) of a jumping, 21O-l-'g Ilea yielded the data used to plot the graph given in Fig. 2.42. (See "The Flying Leap of the Flea" by M.
The graph in Figure describes the acceleration as a function of time for a stone rolling down a hill starting from rest. (a) Find the change in the stone's velocity between t = 2.5 s and t = 7.5
On a 20-mile bike ride, you ride the first 10 miles at an average speed of 8 mi/b. What must your average speed over the next 10 miles be to have your average speed for the total 20 miles be (a) 4
The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00m/S3)t3 - (10.0m/s2 )t2 + (9.00m/s)t. (a) Draw the x-t, v.-t, and az-f graphs of this particle. (b) At what time(s)
Relay Race In a relay race, each contestant runs 25.0 m while carrying an egg balanced on a spoon, turns around, and comes back to the starting point. Edith runs the first 25.0 m in 20.0 s. On the
Dan gets on Interstate Highway 1-80 at Seward, Nebraska, and drives due west in a straight line and at an average velocity of magnitude 88 km/h. After traveling 76 Ian he reaches the Aurora exit
Freeway TraI1ic According to a Scientific American article (May 1990), current freeways can sustain about 2400 vehicles per lane per hour in smooth traffic flow at 96 km/b (60 m/b). With more
A world-class sprinter accelerates to his maximum speed in 4.0 s. He then maintains this speed for the remainder of a 9.1-m race, finishing with a total time of 9.1 s. (a) What is the runner's
A sled starts from rest at the top of a hill and slides down with a constant acceleration. At some later time it is 14.4 m from the top; 2.00 s after that it is 25.6 m from the top, 2.00s later 40.0
A gazelle is running in a straight line (the x-axis). The graph in Fig. 2.45 shows this animal's velocity as a function of time. During the first 12.0 s, find(a) The total distance moved and(b) The
In air or vacuum light travels at a constant speed of 3.0 X 10" m/s. To answer some of these questions you may need to look up astronomical data in Appendix F. (a) One light year is defined as the
Use the information in Appendix F to answer the questions. (a) What is the speed of the Galapagos Islands, on the earth's equator, due to our planet's spin on its axis? (b) What is the earth's
A rigid ball traveling in a straight line (the x-axis) hits a solid wall and suddenly rebounds during a brief instant. The v,-t graph in Fig. 2.46 shows this hall's velocity as a function of time.
A hall starts from rest and rolls down a hill with uniform acceleration, traveling 150 m during the second 5.0 s of its motion. How far did it roll during the first 5.0 s of motion?
Collision the engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track (Fig. 2.47). The freight train is traveling at 15.0 m/s in the
Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant 1.50 m}s. If you start 0.90 m
Two cars start 200 m apart and drive toward each other at a steady 10 m}s. On the front of one of them, an energetic grasshopper jumps back and forth between the cars (he has strong legs!) with a
An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s2, and the automobile
Two stunt drivers drive directly toward each other. At time t = 0 the two cars are a distance D apart, car 1 is at rest, and car 2 is moving to the left with speed Va. Car 1 begins to move at t = 0,
A marble is released from one rim of a hemispherical bowl of diameter 50.0 cm and rolls down and up to the opposite rim in 10.0 s. Find (a) The average speed and (b) The average velocity of the
You may have noticed while driving that your car's velocity does not continue to increase, even though you keep your foot on the gas pedal. This behavior is due to air resistance and friction between
Passing the driver of a car wishes to pass a truck that is traveling at a constant speed of 20.0 m/s (about 45 mi/h). Initially, the car is also traveling at 20.0 m/s and its front bumper is 24.0 m
An object's velocity is measured to be vx (t) = a - pt', where a = 4.00 m/s and p = 2.00 m/S3. At t = 0 the object is at x = O. (a) Calculate the object's position and acceleration as functions of
The acceleration of a particle is given by ax< t) = -2. (JOm/S2 + (3.oom/s3)t. (a) Find the initial velocity vax such that the particle will have the same x-coordinate at t = 4.00 s as it had at t
Egg Drop you are on the roof of the physics building. 46.0 m above the ground (Fig 2.49) your physics professor, who is 1.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s.
A certain volcano on earth can eject rocks vertically to a maximum height H.(a) How high (in terms of If) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The
An entertainer juggles balls while doing other activities. In one act, she throws a ball vertically upward, and while it is in the air, she runs to and from a table 5.50 m away at a constant speed of
Visitors at an amusement park watch divers step off a platform 21.3 m (70 ft) above a pool of water. According to the announcer, the divers enter the water at a speed of 56 mi/h (25 m/s). Air
A flowerpot falls off a windowsill and falls past the window below. You may ignore air resistance. It takes the pot 0.420 s to pass this window, which is 1.90 m high. How far is the top of the window
Certain rifles can fire a bullet with a speed of 965 m/s just as it leaves the muzzle (this speed is called the muzzle velocity). If the muzzle is 70.0 cm long and if the bullet is accelerated
A Multi-stage Rocket In the first stage of a two-stage rocket, the rocket is fired from the launch pad starting from rest but with a constant acceleration of 3.50 m/s2 upward. At 25.0 s after launch,
Look Out Below. Sam heaves a 16-lb shot straight upward, giving it a constant upward acceleration from rest of 45.0 m/s' for 64.0 cm. He releases it 2.20 m above the ground. You may ignore air
A physics teacher performing an outdoor demonstration suddenly falls from rest off a high cliff and simultaneously shouts "Help." When she has fallen for 3.0 s, she hears the echo of her shout from
Juggling Act a juggler performs in a room whose ceiling is 3.0 m above the level of his hands. He throws a ball upward so that it just reaches the ceiling. (a) What is the initial velocity of the
A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 5.0 m/s'. Secret agent Austin Powers jump on just as the helicopter lifts off the ground. Meter the two men struggle
Building Height Spider-Man steps from the top of a tall bni1ding. He falls freely from rest to the ground a distance of h. He falls a distance of hl4 in the last 1.0 s of his fall. What is the height

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