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physics
mechanics

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Are any of the vectors in Fig. 3.23 equal?
An airplane climbs at an angle of with a horizontal component of speed of 200 km/h. (a) What is the plane’s actual speed? (b) What is the magnitude of the vertical component of its velocity?
A hot air balloon rises vertically with a speed of 1.5 m/s. At the same time, there is a horizontal wind blowing. In which direction is the balloon moving?
During part of its trajectory (which lasts exactly 1 min) a missile travels at a constant speed of while maintaining a constant orientation angle of from the vertical. (a) During this phase, what is true about its velocity components: (1) vy > vx, (2) vy = vx, or (3) vy < vx? (b) Determine the
At the instant a ball rolls off a rooftop it has a horizontal velocity component of +10.0 m/s and a vertical component (downward) of 15.0 m/s. (a) Determine the angle of the roof. (b) What is the ball’s speed as it leaves the roof?
A particle moves at a speed of 3.0 m/s in the + x-direction. Upon reaching the origin, the particle receives a continuous constant acceleration of 0.75 m/s2 in the – y-direction. What is the position of the particle 4.0 s later?
At a constant speed of 60 km/h, an automobile travels 700 m along a straight highway that is inclined 4.0o to the horizontal. An observer notes only the vertical motion of the car. What is the car’s (a) Vertical velocity magnitude and (b) Vertical travel distance?
A baseball player hits a home run into the right field upper deck. The ball lands in a row that is 135 m horizontally from home plate and 25.0 m above the playing field. An avid fan measures its time of flight to be 4.10 s. (a) Determine the ball’s average velocity components. (b) Determine the
Using the triangle method, show graphically that (a) A-bar + B-bar = B-bar + A-bar and (b) If A-bar – B-bar = C-bar, then A-bar = B-bar + C-bar
(a) Is vector addition associative? That is, does (A-bar + B-bar) + C-bar = A-bar + (B-bar + C-bar)? (b) Justify your answer graphically.
(a) What is the sum of A-bar = 3.0 x + 5.0 y and B-bar = 1.0 x – 3.0 y-bar? (b) What are the magnitude and direction of A-bar of B-bar?
A golf ball is hit with an initial speed of at an angle less than 45o above the horizontal. (a) The horizontal velocity component is (1) greater than, (2) equal to, (3) less than the vertical velocity component. Why? (b) If the ball is hit at an angle of 37o, what are the initial horizontal and
For the two vectors and x-bar1 = (20m)x-bar and x-bar2 = (15m) x-bar, compute and show graphically (a) x-bar1 + x-bar2, (b) x-bar1 – x-bar2, (c) x-bar2 – x-bar1,
If the vector is added to vector, the result is. If is subtracted from, the result is. What is the magnitude of A-bar?
Two boys are pulling a box across a horizontal floor as shown in Fig 3.26. If F1 = 50.0 N and F2 = 100N, find the resultant (or sum) force by(a) The graphical method and(b) The component method.
For each of the given vectors, give a vector that, when added to it, yields a null vector (a vector with a magnitude of zero). Express the vector in the form other than that in which it is given (component or magnitude– angle): (a) A-bar = 4.5 cm, 40o above the +x-axis; (b) B-bar = (2.0 cm)
(a) If each of the two components (x and y) of a vector are doubled, (1) the vector’s magnitude doubles, but the direction remains unchanged; (2) the vector’s magnitude remains unchanged, but the direction angle doubles; or (3) both the vector’s magnitude and direction angle double. (b) If
Two vectors are given by A-bar = 4.0 X-bar – 2.0 y-bar and B-bar = 1.0 x-bar + 5.0 y-bar. What is (a) A-bar + B-bar, (b) B-bar – A-bar, and (c) A vector such that A-bar + B-bar + C-bar = 0?
Two brothers are pulling their other brother on a sled (Fig 3.27).(a) Find the resultant (or sum) of the vectors F-bar1 and F-bar2(b) If F-bar1 in the figure were at an angle of 27o instead of 37o with the +x-axis, what would be the resultant (or sum) of F-bar1 and F-bar2?
Given two vectors, which has a length of 10.0 and makes an angle of 45o below the –x-axis, and which has an x-component of +2.0 and a y-component of +4.0, (a) Sketch the vectors on x– y axes, with all their “tails” starting at the origin, and (b) Calculate A-bar + B-bar.
The velocity of object 1 in component form is v-bar = (+2.0 m/s)x-bar + (–4.0 m/s) y-bar. Object 2 has twice the speed of object 1 but moves in the opposite direction. (a) Determine the velocity of object 2 in component notation. (b) What is the speed of object 2?
For the vectors shown in Fig. 3.28, determine A-bar + B-bar + C-bar
The x-and y-components of an acceleration vector are 3.0 m/s2 and 4.0 m/s2, respectively. (a) The magnitude of the acceleration vector is (1) less than 3.0 m/s2, (2) between and 3.0 m/s2 and 4.0 m/s2 (3) between and 4.0 m/s2 and 7.0 m/s2 (4) equal to 7.0 m/s2. (b) What are the magnitude and
For the velocity vectors shown in Fig. 3.28, determine A-bar €“ B-bar €“ C-bar.
Given two vectors A-bar and B-bar with magnitudes A and B, respectively, you can subtract B-bar from A-bar to get a third vector C-bar = A-bar - B-bar. If the magnitude of C-bar is equal to C = A + B, what is the relative orientation of A-bar vectors and B-bar?
In two successive chess moves, a player first moves his queen two squares forward, then moves the queen three steps to the left (from the player’s view). Assume each square is 3.0 cm on a side. (a) Using forward (toward the player’s opponent) as the positive y-axis and right as the positive
Referring to the parallelogram in Fig. 3.29, express C-bar, C-bar €“ B-bar, and (E-bar €“ D-bar + C-bar) in terms of and B-bar.
Two force vectors, F-bar = (3.0 N) x-bar – (4.0 N) y-bar and F-bar = (-6.0 N)x-bar + (4.5 N) y-bar, are applied to a particle. What third force F-bar3 would make the net, or resultant, force on the particle zero?
A student works three problems involving the addition of two different vectors F-bar1 and F-bar2. He states that the magnitudes of the three resultants are given by (a) F1 + F2, (b) F1 – F2,and (c) √F21 + F22. Are these results possible? If so, describe the vectors in each case.
A block weighing 50 N rests on an inclined plane. Its weight is a force directed vertically downward, as illustrated in Fig. 3.30. Find the components of the force parallel to the surface of the plane and perpendicular to it.
Two displacements, one with a magnitude of 15.0 m and a second with a magnitude of 20.0 m, can have any angle you want. (a) How would you create the sum of these two vectors so it has the largest magnitude possible? What is that magnitude? (b) How would you orient them so the magnitude of the sum
A person walks from point A to point B as shown in Fig. 3.31. What is the person€™s displacement relative to point A?
A meteorologist tracks the movement of a thunderstorm with Doppler radar. At 8: 00 PM, the storm was 60 mi northeast of her station. At 10:00 PM, the storm is at 75 mi north. (a) The general direction of the thunder-storm’s velocity is (1) south of east, (2) north of west, (3) north of east, (4)
If the magnitude of a velocity vector is 7.0 m/s and the x-component is 3.0 m/s, what is the y-component?
A flight controller determines that an airplane is 20.0 mi south of him. Half an hour later, the same plane is 35.0 mi northwest of him. (a) The general direction of the airplane’s velocity is (1) east of south, (2) north of west, (3) north of east, (4) west of south. (b) If the plane is flying
Fig. 3.32 depicts a decorative window (the thick inner square) weighing 100 N suspended in a patio opening (the thin outer square). The upper two corner cables are each at and the left one exerts a force (F1) of 100 N on the window.(a) How does the magnitude of the force exerted by the upper right
A golfer lines up for her first putt at a hole that is 10.5 m exactly northwest of her ball’s location. She hits the ball 10.5 m and straight, but at the wrong angle, 40o from due north. In order for the golfer to have a “two-putt green,” determine (a) The angle of the second putt and (b)
Two students are pulling a box as shown in Fig. 3.26, where and F1 = 100 N F2 = 150 N. What third force would cause the box to be stationary when all three forces are applied?
A ball with a horizontal speed of rolls off a bench 2.0 m high. (a) How long will the ball take to reach the floor? (b) How far from a point on the floor directly below the edge of the bench will the ball land?
An electron is ejected horizontally at a speed of 1.5 x 106 m/s from the electron gun of a computer monitor. If the viewing screen is 35 cm from the end of the gun, how far will the electron travel in the vertical direction before hitting the screen? Based on your answer, do you think designers
A ball rolls horizontally with a speed of 7.6 m/s off the edge of a tall platform. If the ball lands 8.7 m from the point on the ground directly below the edge of the plat-form, what is the height of the platform?
A ball is projected horizontally with an initial speed of 5.0 m/s. Find its (a) Position and (b) Velocity at t = 25s.
An artillery crew wants to shell a position on level ground 35 km away. If the gun has a muzzle velocity of 770 m/s, to what angle of elevation should the gun be raised?
A pitcher throws a fastball horizontally at a speed of 140 km/h toward home plate, 18.4 m away. (a) If the batter’s combined reaction and swing times total 0.350 s, how long can the batter watch the ball after it has left the pitcher’s hand before swinging? (b) In traveling to the plate, how
The x-component of a velocity vector that has an angle of to the has a magnitude of 4.8 m/s. (a) What is the magnitude of the velocity? (b) What is the magnitude of the y-component of the velocity?
Ball A rolls at a constant speed of 0.25 m/s on a table 0.95 m above the floor, and ball B rolls on the floor directly under the first ball with the same speed and direction. (a) When ball A rolls off the table and hits the floor, (1) ball B is ahead of ball A, (2) ball B collides with ball A, (3)
The pilot of a cargo plane flying 300 km/h at an altitude of 1.5 km wants to drop a load of supplies to campers at a particular location on level ground. Having the designated point in sight, the pilot prepares to drop the supplies. (a) What should the angle be between the horizontal and the
A wheeled car with a spring-loaded cannon fires a metal ball vertically (Fig. 3.24). If the vertical initial speed of the ball is as the cannon moves horizontally at a speed of 0.75 m/s, (a) How far from the launch point does the ball fall back into the cannon, and (b) What would happen if the
A convertible travels down a straight, level road at a slow speed of 13 km/h. A person in the car throws a ball with a speed of 3.6 m/s forward at an angle of to the horizontal. Where is the car when the ball lands?
A good-guy stuntman is being chased by bad guys on a building’s level roof. He comes to the edge and is to jump to the level roof of a lower building 4.0 m below and 5.0 m away. What is the minimum launch speed the stunt-man needs to complete the jump? (Landing on the edge is assumed complete.)
An astronaut on the Moon fires a projectile from a launcher on a level surface so as to get the maximum range. If the launcher gives the projectile a muzzle velocity of 25m/s, what is the range of the projectile?
In 2004 two Martian probes successfully landed on the Red Planet. The final phase of the landing involved bouncing the probes until they came to rest (they were surrounded by protective inflated “balloons”). During one of the bounces, the telemetry (electronic data sent back to Earth) indicated
In laboratory situations, a projectile’s range can be used to determine its speed. To see how this is done, sup-pose a ball rolls off a horizontal table and lands 1.5 m out from the edge of the table. If the tabletop is 90 cm above the floor, determine (a) The time the ball is in the air, and
A stone thrown off a bridge 20 m above a river has an initial velocity of 12m/s at an angle of 45o above the horizontal (Fig. 3.33).(a) What is the range of the stone? (b) At what velocity does the stone strike the water?
If the maximum height reached by a projectile launched on level ground is equal to half the projectile’s range, what is the launch angle?
A student walks 100 m west and 50 m south. (a) To get back to the starting point, the student must walk in a general direction of (1) south of west, (2) north of east, (3) south of east, (4) north of west. (b) What displacement will bring the student back to the starting point?
William Tell is said to have shot an apple off his son’s head with an arrow. If the arrow was shot with an initial speed of 55 m/s and the boy was 15 m away, at what launch angle did Bill aim the arrow? (Assume that the arrow and apple are initially at the same height above the ground.)
This time, William Tell is shooting at an apple that hangs on a tree (Fig. 3.34). The apple is a horizontal distance of 20.0 m away and at a height of 4.00 m above the ground. If the arrow is released from a height of 1.00 m above the ground and hits the apple 0.500 s later, what is the
The apparatus for a popular lecture demonstration is shown in Fig. 3.35. A gun is aimed directly at a can, which is released at the same time that the gun is fired.This gun won€™t miss as long as the initial speed of the bullet is sufficient to reach the falling target before the target
A shot-putter launches the shot from a vertical distance of 2.0 m off the ground (from just above her ear) at a speed of 12.0 m/s. The initial velocity is at an angle of above the horizontal. Assume the ground is flat. (a) Compared to a projectile launched at the same angle and speed at ground
A ditch 2.5 m wide crosses a trail bike path (Fig 3.36). An upward incline of 15o has been built on the approach so that the top of the incline is level with the top of the ditch. What is the minimum speed a trail bike must be moving to clear the ditch? (Add 1.4 m to the range for the back of the
A ball rolls down a roof that makes an angle of to the horizontal (Fig. 3.37). It rolls off the edge with a speed of 5.00 m/s. The distance to the ground from that point is two stories or 7.00 m.(a) How long is the ball in the air?(b) How far from the base of the house does it land?(c) What is its
A quarterback passes a football—at a velocity of 50 ft/s at an angle of 40o to the horizontal—toward an intended receiver 30 yd downfield. The pass is released 5.0 ft above the ground. Assume that the receiver is stationary and that he will catch the ball if it comes to him. Will the pass be
A 2.05-m-tall basketball player takes a shot when he is 6.02 m from the basket (at the three-point line). If the launch angle is 25o and the ball was launched at the level of the player’s head, what must be the release speed of the ball for the player to make the shot? The basket is 3.05 m above
While you are traveling in a car on a straight, level interstate highway at 90 km/h, another car passes you in the same direction; its speedometer reads 120 km/h. (a) What is your velocity relative to the other driver? (b) What is the other car’s velocity relative to you?
A shopper is in a hurry to catch a bargain in a department store. She walks up the escalator, rather than let-ting it carry her, at a speed of 10 m relative to the escalator. If the escalator is 10 m long and moves at a speed of 0.50 m/s, how long does it take for the shopper to get to the next
A student strolls diagonally across a level rectangular campus plaza, covering the 50-m distance in 1.0 min (Fig. 3.25).(a) If the diagonal route makes a angle with the long side of the plaza, what would be the distance traveled if the student had walked halfway around the outside of the plaza
A motorboat’s speed in still water is 2.0 m/s. The driver wants to go directly across a river with a current speed of 1.5 m/s. At what angle upstream should the boat be steered?
A person riding in the back of a pickup truck traveling at 70 km/h on a straight, level road throws a ball with a speed of 15 km/h relative to the truck in the direction opposite to the truck’s motion. What is the velocity of the ball? (a) Relative to a stationary observer by the side of the
In Exercise 71, what are the relative velocities if the ball is thrown in the direction of the truck? In exercise A person riding in the back of a pickup truck traveling at 70 km/h on a straight, level road throws a ball with a speed of 15 km/h relative to the truck in the direction opposite to the
In a 500-m stretch of a river, the speed of the current is a steady 5.0 m/s. How long does a boat take to finish a round trip (upstream and downstream) if the speed of the boat is 7.5 m/s relative to still water?
A moving walkway in an airport is 75 m long and moves at a speed of 0.60 m/s. A passenger, after traveling 25 m while standing on the walkway, starts to walk at a speed of 0.50 m/s relative to the surface of the walk-way. How long does she take to travel the total distance of the walkway?
A swimmer swims north at 0.15 m/s relative to still water across a river that flows at a rate of 0.20 m/s from west to east. (a) The general direction of the swimmer’s velocity, relative to the riverbank, is (1) north of east, (2) south of west, (3) north of west, (4) south of east. (b)
A boat that travels at a speed of 6.75 m/s in still water is to go directly across a river and back (Fig. 3.38). The current flows at 0.50 m/s.(a) At what angle(s) must the boat be steered?(b) How long does it take to make the round trip? (Assume that the boat€™s speed is constant at all
A pouring rain comes straight down with a raindrop speed of 6.0 m/s. A woman with an umbrella walks east-ward at a brisk clip of 1.5 m/s to get home. At what angle should she tilt her umbrella to get the maximum protection from the rain?
It is raining, and there is no wind. When you are sitting in a stationary car, the rain falls straight down relative to the car and the ground. But when you’re driving, the rain appears to hit the windshield at an angle. (a) As the velocity of the car increases, this angle (1) also increases,
If the flow rate of the current in a straight river is greater than the speed of a boat in the water, the boat cannot make a trip directly across the river. Prove this statement.
A ball rolls at a constant velocity of 1.50 m/s at an angle of 45o below the in the fourth quadrant. If we take the ball to be at the origin at t = 0 what are its coordinates (x, y) 1.65 s later?
You are in a fast powerboat that is capable of a sustained steady speed of 20.0 m/s in still water. On a swift, straight section of a river you travel parallel to the bank of the river. You note that you take 15.0 s to go between two trees on the riverbank that are 400 m apart. (a) (1) Are you
An observer by the side of a straight, level, north-south road watches a car (A) Moving south at a rate of 75 km/h. A driver in another car (B) Going north at 50 km/h also observes car A. (a) What is car A’s velocity as observed from car B? (Take north to be positive.) (b) If the roadside
An airplane flies due north with an air speed of 250 km/h. A steady wind at 75 km/h blows eastward. (Air speed is the speed relative to the air.) (a) What is the plane’s ground speed (vpg)? (b) If the pilot wants to fly due north, what should his heading be?
A shopper in a mall is on an escalator that is moving downward at an angle of 41.8o below the horizontal at a constant speed of 0.75 m/s. At the same time a little boy drops a toy parachute from a floor above the escalator and it descends at a steady vertical speed of 0.50 m/s. Determine the speed
An airplane is flying at 150 mi/h (its speed in still air) in a direction such that with a wind of 60.0 mi/h blowing from east to west, the airplane travels in a straight line southward. (a) What must be the plane’s heading (direction) for it to fly directly south? (b) If the plane has to go
A hockey puck slides along a horizontal ice surface at 20.0 m/s, hits a flat vertical wall, and bounces off. Its initial velocity vector makes an angle of 35o with the wall and it comes off at an angle of 25o moving at 10.0 m/s. Choose the to be along the wall in the direction of motion and the
A football is kicked off the flat ground at 25.0 m/s at an angle of 30o relative to the ground. (a) Determine the total time it is in the air. (b) Find the angle of its velocity with respect to the ground after it has been in the air for one-fourth of this time. (c) Repeat for one-half and
A railroad flatbed car is set up for a physics demonstration. It is set to roll horizontally on its straight rails at a constant speed of 12.0 m/s. On it is rigged a small launcher capable of launching a small lead ball vertically upward, relative to the bed of the car, at a speed of 25.0 m/s. (a)
A sailboat is traveling due north at 2.40 m/s on a calm lake with no noticeable water currents. From the crow’s nest at the top of its 10.0-m-high mast, one of the passengers drops her digital camera. (a) Make a sketch of the camera’s trajectory from the point of view of the passengers on the
At a merging on-ramp of a busy Los Angeles freeway, car A is moving directly east on the freeway at a steady speed of 35.0 m/s. Car B is merging onto the freeway from the on-ramp, which points north of due east, moving at 30.0 m/s. (Fig. 3.39.) If the two cars collide, it will be at the point
A ball rolling on a table has a velocity with rectangular components vx = 0.60 m/s and vy = 0.80 m/s. What is the displacement of the ball in an interval of 2.5 s?
(a) As a weightlifter lifts a barbell from the floor in the €œclean€ procedure (Fig. 5.25a), has he done work? Why or why not?(b) In raising the barbell above his head in the €œjerk€ procedure, is he doing work? Explain. (c) In holding the barbell above
A certain amount of work W is required to accelerate a car from rest to a speed v. If instead an amount of work equal to 2Wis done on the car, what is the car’s speed?
Car B is traveling twice as fast as car A, but car A has four times the mass of car B. Which car has the greater kinetic energy?
A lab notebook sits on a table 0.75 m above the floor. Your lab partner tells you the book has zero potential energy, and another student says it has 8.0 J of potential energy. Who is correct?
When you throw an object into the air, is its initial speed the same as its speed just before it returns to your hand? Explain by applying the concept of conservation of mechanical energy.
A student throws a ball vertically upward so it just reaches the height of a window on the second floor of a dormitory. At the same time that the ball is thrown upward, a student at the window drops an identical ball. Are the mechanical energies of the balls the same at half the height of the
If you check your electricity bill, you will note that you are paying the power company for so many kilowatt-hours (kWh). Are you really paying for power? Explain.
(a) Does efficiency describe how fast work is done? Explain. (b) Does a more powerful machine always per-form more work than a less powerful one? Explain.
You are carrying a backpack across campus. What is the work done by your vertical carrying force on the back-pack? Explain.
A jet plane flies in a vertical circular loop. In what regions of the loop is the work done by the force of gravity on the plane positive negative? Is the work constant? If not, are there maximum and minimum instantaneous values? Explain.
When walking up stairs, it is easier to do so in a zigzag path rather than going straight up. Why is this?

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