Question: A boy throws a baseball onto a

> Which of the following objects can’t be accelerating? (a) An object moving with a constant speed (b) An object moving with a constant velocity or (c) An object moving along a curve.

> A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle u above the horizontal (Fig. 4.76). She pulls on the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. (a) Draw a free-bod

> (a) What is the resultant force exerted by the two cables supporting the traffic light in Figure P4.75? (b) What is the weight of the light? Figure P4.75:

> (a) What is the minimum force of friction required to hold the system of Figure P4.74 in equilibrium? (b) What coefficient of static friction between the 100.-N block and the table ensures equilibrium? (c) If the coefficient of kinetic friction between t

> Three objects are connected on a table as shown in Figure P4.73. The coefficient of kinetic friction between the block of mass m2 and the table is 0.350. The objects have masses of m1 = 4.00 kg, m2 = 1.00 kg, and m3 = 2.00 kg as shown, and the pulleys ar

> As a protest against the umpire’s calls, a baseball pitcher throws a ball straight up into the air at a speed of 20.0 m/s. In the process, he moves his hand through a distance of 1.50 m. If the ball has a mass of 0.150 kg, find the force he exerts on the

> Two blocks each of mass m = 3.50 kg are fastened to the top of an elevator as in Figure P4.56. (a) If the elevator has an upward acceleration a = 1.60 m/s2, find the tensions T1 and T2 in the upper and lower strings. (b) If the strings can withstand a ma

> Objects of masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.70. The object m1 is held at rest on the floor, and m2 rests on a fixed incline of θ = 40.0°. T

> The average person passes out at an acceleration of 7g (that is, seven times the gravitational acceleration on Earth). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest to 60.0 miles

> A 15.0-lb block rests on a horizontal floor. (a) What force does the floor exert on the block? (b) A rope is tied to the block and is run vertically over a pulley. The other end is attached to a free-hanging 10.0-lb object. What now is the force exerted

> A block of mass 3m is placed on a frictionless horizontal surface, and a second block of mass m is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude F is applied to the first block as in Figure P4.68. (

> In Figure P4.64, m1 = 10. kg and m2 = 4.0 kg. The coefficient of static friction between m1 and the horizontal surface is 0.50, and the coefficient of kinetic friction is 0.30. (a) If the system is released from rest, what will its acceleration be? (b) I

> Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley, as in Figure P4.66. Determine (a) The tension in the string, (b) The acceleration of each object, and (c) The distance each object will

> Objects with masses m1 = 10.0 kg and m2 = 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.64. If, when the system starts from rest, m2 falls 1.00 m in 1.20 s, determine the coefficient of kinetic friction be

> An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg, as shown in Figure P4.64. Find (a) The acceleration of each o

> In Figure P4.63, the light, taut, unstretchable cord B joins block 1 and the larger-mass block 2. Cord A exerts a force on block 1 to make it accelerate forward. (a) How does the magnitude of the force exerted by cord A on block 1 compare with the magnit

> Two blocks of masses m1 and m2 (m1 > m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1 in Figure P4.62. (a) If P is the magnitude of the contact force between the bl

> A 1.00 x 103 car is pulling a 300.-kg trailer. Together, the car and trailer have an acceleration of 2.15 m/s2 in the positive x - direction. Neglecting frictional forces on the trailer, determine (a) The net force on the car, (b) The net force on the tr

> Two packing crates of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.60. The 5.00-kg crate lies on a smooth incline of angle 40.0°. Find (a) The acceleration of the 5.00-kg cra

> A 50.0-g Super Ball traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average acceleration of the ball during

> The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of power roller skates, which provide a constant horizontal acceleration of 15.0 m/s2, as shown in Figure P3.59. The coyote starts off at

> A football receiver running straight downfield at 5.50 m/s is 10.0 m in front of the quarterback when a pass is thrown downfield at 25.0° above the horizon (Fig. P3.58). If the receiver never changes speed and the ball is caught at the same he

> One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both

> Antlion larvae lie in wait for prey at the bottom of a conical pit about 5.0 cm deep and 3.8 cm in radius. When a small insect ventures into the pit, it slides to the bottom and is seized by the antlion. If the prey attempts to escape, the antlion rapidl

> A golf ball with an initial speed of 50.0 m/s lands exactly 240 m downrange on a level course. (a) Neglecting air friction, what two projection angles would achieve this result? (b) What is the maximum height reached by the ball, using the two angles det

> A landscape architect is planning an artificial waterfall in a city park. Water flowing at 0.750 m/s leaves the end of a horizontal channel at the top of a vertical wall h = 2.35 m high and falls into a pool (Fig. P3.54). (a) How far from the wall will

> A celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.2 m have been recorded. If a frog jumps 2.2 m and the launch angle is 45°, find (a) The frog’s launch speed (b) The time

> If raindrops are falling vertically at 7.50 m/s, what angle from the vertical do they make for a person jogging at 2.25 m/s?

> A daredevil is shot out of a cannon at 45.0° to the horizontal with an initial speed of 25.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevi

> Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behaviour is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 45°, sails through the

> A particle starts from rest and accelerates as shown in Figure P2.20. Determine (a) The particle’s speed at t = 10.0 s and at t = 20.0 s, and (b) The distance traveled in the first 20.0 s.

> Construct motion diagrams showing the velocity and acceleration of a projectile at several points along its path, assuming (a) The projectile is launched horizontally (b) The projectile is launched at an angle θ with the horizontal.

> A hunter wishes to cross a river that is 1.5 km wide and flows with a speed of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for cr

> When baseball outfielders throw the ball, they usually allow it to take one bounce, on the theory that the ball arrives at its target sooner that way. Suppose that, after the bounce, the ball rebounds at the same angle θ that it had when it

> Spitting cobras can defend themselves by squeezing muscles around their venom glands to squirt venom at an attacker. Suppose a spitting cobra rears up to a height of 0.500 m above the ground and launches venom at 3.50 m/s, directed 50.0° above the horizo

> The x - and y - coordinates of a projectile launched from the origin are x = υ0xt and y = υ0yt – 1/2 gt2. Solve the first of these equations for time t and substitute into the second to show that the path of a projectile is a parabola with the form y = a

> A quarterback throws a football toward a receiver with an initial speed of 20. m/s at an angle of 30° above the horizontal. At that instant the receiver is 20. m from the quarterback. In (a) What direction and (b) With what constant speed should the rece

> A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in Figure P3.44. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoo

> A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of 35° to the horizontal, and air resistance is negligible. Find (a) The initial speed of the ball (b) The time it

> A ball is thrown straight upward and returns to the thrower’s hand after 3.00 s in the air. A second ball thrown at an angle of 30.0° with the horizontal reaches the same maximum height as the first ball. (a) At what speed was the first ball thrown? (b)

> (a) If a person can jump a maximum horizontal distance (by using a 45° projection angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2? (b) Repeat for Mars, where the acceleratio

> A farm truck travels due east with a constant speed of 9.50 m/s along a horizontal road. A boy riding in the back of the truck tosses a can of soda upward (Fig. P3.40) and catches it at the same location in the truck bed, but 16.0 m farther down the road

> Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/h due east. Runner B is initially 3.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the

> A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100. m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to mo

> Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. One paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. With downstream as the positive d

> A father demonstrates projectile motion to his children by placing a pea on his fork’s handle and rapidly depressing the curved tines, launching the pea to heights above the dining room table. Suppose the pea is launched at 8.25 m/s at an angle of 75.0°

> In a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the counter and strikes the floor at distance d from the base of the counter. If the height of the counter is h, (a) find an expression for the time

> Towns A and B in Figure P3.35 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/

> You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v( at an angle θ with respect to the horizontal. Let the buildin

> A moving walkway at an airport has a speed υ1 and a length L. A woman stands on the walkway as it moves from one end to the other, while a man in a hurry to reach his flight walks on the walkway with a speed of υ2 relative to the moving walkway. (a) How

> How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars’ front bumpers are initially 100 m apart?

> This is a symbolic version of Problem 29. A river has a steady speed of Ï…s. A student swims upstream a distance d and back to the starting point. (a) If the student can swim at a speed of Ï… in still water, how much time tup does it

> A race car moves such that its position fits the relationship x = (5.0 m/s)t + (0.75 m/s3)t3 Where x is measured in meters and t in seconds. (a) Plot a graph of the car’s position versus time. (b) Determine the instantaneous velocity of the car at t 5 4.

> A river has a steady speed of 0.500 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in

> A bomber is flying horizontally over level terrain at a speed of 275 m/s relative to the ground and at an altitude of 3.00 km. (a) The bombardier releases one bomb. How far does the bomb travel horizontally between its release and its impact on the groun

> Suppose a chinook salmon needs to jump a waterfall that is 1.50 m high. If the fish starts from a distance 1.00 m from the base of the ledge over which the waterfall flows (a) find the x - and y - components of the initial velocity the salmon would need

> An airplane maintains a speed of 630 km/h relative to the air it is flying through, as it makes a trip to a city 750 km away to the north. (a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 km/h toward t

> A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50 m/s2. (a) What is the acceleration of the bolt relative to the train car? (b) What is the acceleration of the bolt relative to the Earth? (c) Describe th

> A Coast Guard cutter detects an unidentified ship at a distance of 20.0 km in the direction 15.0° east of north. The ship is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat to intercept and investigat

> A jet airliner moving initially at 3.00 x 102 mi/h due east enters a region where the wind is blowing 1.00 x 102 mi/h in a direction 30.0° north of east. (a) Find the components of the velocity of the jet airliner relative to the air, v(JA. (b

> A car travels due east with a speed of 50.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 60.0° with the vertical. Find the velocity of the rai

> Suppose a boat moves at 12.0 m/s relative to the water. If the boat is in a river with the current directed east at 2.50 m/s, what is the boat’s speed relative to the ground when it is heading (a) East, with the current (b) West, against the current?

> A cruise ship sails due north at 4.50 m/s while a Coast Guard patrol boat heads 45.0° north of west at 5.20 m/s. What are (a) the x – component (b) y - component of the velocity of the cruise ship relative to the patrol boat?

> A graph of position versus time for a certain particle moving along the x - axis is shown in Figure P2.6. Find the instantaneous velocity at the instants (a) t = 1.00 s (b) t = 3.00 s (c) t = 4.50 s, and (d) t = 7.50 s. Figure P2.6

> A playground is on the flat roof of a city school, 6.00 m above the street below (Fig. P3.19). The vertical wall of the building is h 5 7.00 m high, to form a 1-m-high railing around the playground. A ball has fallen to the street below, and a passer-by

> A fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of θi = 30.0° above the horizontal as shown in Figure P3.18. If the speed of the stream as it leaves the hose is

> A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0° above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile’s velocity at the highest point of its trajectory? (b)

> An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x - and y - coordinates of the shell where it explodes, relative to its

> A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a cons

> From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.00 m/s and angle of 20.0° below the horizontal. It strikes the ground 3.00 s later. (a) If the base of the building is taken to be the origin

> A brick is thrown upward from the top of a building at an angle of 25° to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building?

> The record distance in the sport of throwing cowpats is 81.1 m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) The initial speed of the projecti

> A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0° to t

> A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal range R. (a) At what angle θ is the rock thrown? (b) In terms of the original range R, what is the range Rmax the rock can attain

> A paper in the journal Current Biology tells of some jellyfish-like animals that attack their prey by launching stinging cells in one of the animal kingdom’s fastest movements. High-speed photography showed the cells were accelerated from rest for 700. n

> The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height?

> One of the fastest recorded pitches in major league baseball, thrown by Tim Lin cecum in 2009, was clocked at 101.0 mi/h (Fig. P3.8). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached ho

> A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in Figure P3.7. (a) What are the coordinates of the initial position of the ston

> A rabbit is moving in the positive x - direction at 2.00 m/s when it spots a predator and accelerates to a velocity of 12.0 m/s along the negative y - axis, all in 1.50 s. Determine (a) The x – component (b) The y - component of the rabbit’s acceleration

> A car is traveling east at 25.0 m/s when it turns due north and accelerates to 35.0 m/s, all during a time of 6.00 s. Calculate the magnitude of the car’s average acceleration.

> An ant crawls on the floor along the curved path shown in Figure P3.4. The ant’s positions and velocities are indicated for times ti = 0 and tf = 5.00 s. Determine the x - and y - components of the ant’s (a) displaceme

> A miniature quadcopter is located at xi = 2.00 m and yi = 4.50 m at t = 0 and moves with an average velocity having components vav,x = 1.50 m/s and vav,y = -1.00 m/s. What are the (a) x – coordinate (b) y - coordinate of the quadcopter’s position at t =

> A hiker walks 2.00 km north and then 3.00 km east, all in 2.50 hours. Calculate the magnitude and direction of the hiker’s (a) Displacement (in km) (b) Average velocity (in km/h) during those 2.50 hours. (c) What was her average speed during the same tim

> As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 61.0 kg. If this

> Consider a solid metal sphere (S) a few centimeters in diameter and a feather (F). For each quantity in the list that follows, indicate whether the quantity is the same, greater, or lesser in the case of S or in that of F. Explain in each case why you ga

> To qualify for the finals in a racing event, a race car must achieve an average speed of 250. km/h on a track with a total length of 1.60 x 103. If a particular car covers the first half of the track at an average speed of 230. km/h, what minimum average

> Four forces act on an object, given by A( =40.0 N east, B( = 50.0 north, C( = 70.0 N west, and D( = 90.0 N south. (a) What is the magnitude of the net force on the object? (b) What is the direction of the force?

> A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 N, how long does it take to increase the speed of the train from rest to 80 km/h?

> Assume the three blocks portrayed in Figure P4.59 move on a frictionless surface and a 42-N force acts as shown on the 3.0-kg block. Determine (a) The acceleration given this system, (b) The tension in the cord connecting the 3.0-kg and the 1.0-kg blocks

> The systems shown in Figure P4.58 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline in Figure P4.58d are frictionless. Figure P4.58:

> Two blocks of masses m and 2m are held in equilibrium on a frictionless incline as in Figure P4.57. In terms of m and θ, find (a) The magnitude of the tension T1 in the upper cord and (b) The magnitude of the tension T2 in the lower cord con

> Two blocks each of mass m are fastened to the top of an elevator as in Figure P4.56. The elevator has an upward acceleration a. The strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b)

> A block of mass m1 = 16.0 kg is on a frictionless table to the left of a second block of mass m2 = 24.0 kg, attached by a horizontal string (Fig. P4.55). If a horizontal force of 1.20 x 102 N is exerted on the block m2 in the positive x - direction, (a)

> An Atwood’s machine (Fig. 4.38) consists of two masses: one of mass 3.00 kg and the other of mass 8.00 kg. When released from rest, what is the acceleration of the system? Figure 4.38:

> A setup similar to the one shown in Figure P4.53 is often used in hospitals to support and apply a traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted on the leg? Ass

> A hockey puck struck by a hockey stick is given an initial speed υ0 in the positive x - direction. The coefficient of kinetic friction between the ice and the puck is µk. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of pa

> Suppose you are driving a car at a high speed. Why should you avoid slamming on your brakes when you want to stop in the shortest possible distance? (Newer cars have antilock brakes that avoid this problem.)

> A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s2, find the force exerted by the rope on the bucket.

> A car is traveling at 50.0 km/h on a flat highway. (a) If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and t

> A bag of sugar weighs 5.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one sixth that on Earth? Repeat for Jupiter, where g is 2.64 times that on Earth. Find the mass of the bag of sugar in kilograms at ea