physics 2001 exam 1

At the top of a cliff a projectile is fired horizontally with some initial velocity, . At the exact same time, an identical projectile is dropped from rest straight down from the same height. Which projectile hits the ground first?

both hit at the same time

A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 26.5 minutes at an average speed of 9.48 m/s. During the second part, she rides for 40.6 minutes at an average speed of 3.21 m/s. Finally, during the third part, she rides for 8.68 minutes at an average speed of 14.9 m/s. (a) How far has the bicyclist traveled during the entire trip? (b) What is the average speed of the bicyclist for the trip?

30652.68 m; 6.74 m/s

A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff. The shell strikes the ground 1330 m from the base of the cliff. The drawing is not to scale. What is the magnitude of the velocity of the shell as it hits the ground?

330 m/s

A dynamite blast at a quarry launches a rock straight upward, and 2.0 s later it is rising at a rate of 15 m/s. Assuming air resistance has no effect on the rock, calculate its speed (a) at launch and (b) 5.2 s after launch.

34.6 m/s; 16.366 m/s

Consider 123 x 3.0 = ? Which of the following answers is correct? Take into account significant digits.

345

Suppose that vectors and have nonzero magnitude. Is it possible for + = 0?

no

A battleship simultaneously fires two artillery shells (projectiles) at enemy ships A and B. If the shells follow the parabolic trajectories shown, which enemy ship gets hit first?

the one being projectile hit farthest

The drawing shows projectile motion at three points along the trajectory. The speeds at the points are v1, v2, and v3. Assume there is no air resistance and rank the speeds, largest to smallest. (Note that the symbol ">" means "greater than".)

v1>v3>v2

Use the component method of vector addition to find the components of the resultant of the four displacements shown in the figure. The magnitudes of the displacements are: A = 2.25 cm, B = 6.35 cm, C = 5.47 cm, and D = 4.19 cm.

x-component: 6.93 cm; y-component: -2.19

An Australian emu is running due north in a straight line at a speed of 13.0 m/s and slows down to a speed of 10.0 m/s in 3.40 s. (a) What is the magnitude and direction of the bird's acceleration? (b) Assuming that the acceleration remains the same, what is the bird's velocity after an additional 1.20 s has elapsed?

-0.8824 m/s2; 8.944 m/s

offers a useful review of the concepts central to this problem. An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of +15.1 m/s and measures a time of 21.7 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet? (positive = up, negative = down)

-1.39 m/s2

Review Conceptual Example 6 as background for this problem. A car is traveling to the left, which is the negative direction. The direction of travel remains the same throughout this problem. The car's initial speed is 17.0 m/s, and during a 3.46-second interval, it changes to a final speed of (a)25.1 m/s and (b)9.57 m/s. In each case, find the acceleration (magnitude and algebraic sign).

-2.34 m/s2; 2.147 m/s2

An object is moving along the x axis. The graph shows its position from the starting point as a function of time. Various segments of the graph are identified by the letters A, B, C, and D.

-3.0 m/s

A cement block accidentally falls from rest from the ledge of a 61.1-m-high building. When the block is 18.6 m above the ground, a man, 1.60 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way?

0.53958 s

provides a review of the concepts that play a role in this problem. A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during (a) segment A, (b) segment B, and (c) segment C?

2;0;3.3;

During his final run, he reached a maximum speed of 632 mph. When the sled's braking system brought it to rest, Colonel Stapp experienced a deceleration of magnitude 46.2g, or 46.2 times the acceleration of gravity at the Earth's surface. Although he survived, he did sustain injuries, such as a fractured wrist, broken ribs, and bleeding in his eyes. Calculate how long it took to bring the rocket sled to rest. Assume the deceleration was constant during the braking period.

0.624 s

A major-league pitcher can throw a ball in excess of 36.4 m/s. If a ball is thrown horizontally at this speed, how much will it drop by the time it reaches a catcher who is 17.0 m away from the point of release?

1.069 m

A woman on a bridge 94.1 m high sees a raft floating at a constant speed on the river below. She drops a stone from rest in an attempt to hit the raft. The stone is released when the raft has 7.78 m more to travel before passing under the bridge. The stone hits the water 2.46 m in front of the raft. Find the speed of the raft.

1.21 m/s

A jogger accelerates from rest to 4.80 m/s in 3.87 s. A car accelerates from 23.3 to 37.6 m/s also in 3.87 s. (a) Find the magnitude of the acceleration of the jogger. (b) Determine the magnitude of the acceleration of the car. (c) How much further does the car travel than the jogger during the 3.87 s?

1.24 m/s2; 3.70 m/s2; 108.4 m

An eagle is flying horizontally at 7.5 m/s with a fish in its claws. It accidentally drops the fish. (a) How much time passes before the fish's speed doubles? (b) How much additional time would be required for the speed to double again?

1.32 s; 1.638 s

A hot-air balloon is rising upward with a constant speed of 2.57 m/s. When the balloon is 6.14 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

1.41 s

The velocity of a train is 80.0 km/h, due west. One and a half hours later its velocity is 65.0 km/h, due west. What is the train's average acceleration?

10.0 km/h2, due east

A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0 s, the x components of the puck's initial velocity and acceleration are v0x = +6.3 m/s and ax = +2.4 m/s2. The y components of the puck's initial velocity and acceleration are v0y = +7.8 m/s and ay = -2.1 m/s2. Find (a) the magnitude v and (b) the direction θ of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis.

10.09 m/s; 41.99 above the x-axis

In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for 0.0836 s, during which time it experiences an acceleration of 233 m/s2. The ball is launched at an angle of 50.6° above the ground. Determine the (a) horizontal and (b) vertical components of the launch velocity.

12.36 m/s; 15.05 m/s

The Space Shuttle travels at a speed of about 9.93 x 103 m/s. The blink of an astronaut's eye lasts about 117 ms. How many football fields (length = 91.4 m) does the Space Shuttle cover in the blink of an eye?

12.7

Ryan throws a tennis ball vertically upward. The ball returns to the point of release after 3.5 s. What is the speed of the ball as it is released?

17 m/s

A golfer hits a shot to a green that is elevated 3.40 m above the point where the ball is struck. The ball leaves the club at a speed of 19.6 m/s at an angle of 46.0˚ above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands.

17.817 m/s

A fire hose ejects a stream of water at an angle of 35.5 ° above the horizontal. The water leaves the nozzle with a speed of 20.2 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

19.69 m

An elevator is moving upward with a speed of 11 m/s. Three seconds later, the elevator is still moving upward, but its speed has been reduced to 5.0 m/s. What is the average acceleration of the elevator during the 3.0 s interval?

2.0 m/s2, downward

A skateboarder, starting from rest, rolls down a 14.7-m ramp. When she arrives at the bottom of the ramp her speed is 8.22 m/s. (a) Determine the magnitude of her acceleration, assumed to be constant. (b) If the ramp is inclined at 29.1 ° with respect to the ground, what is the component of her acceleration that is parallel to the ground?

2.298 m/s2; 2.008 m/s2

(a) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 9.37 m/s when going down a slope for 3.94 s? (b) How far does the skier travel in this time?

2.375 m/s2; 18.46 m

At time t = 0 s, a puck is sliding on a horizontal table with a velocity 3.60 m/s, 35.0° above the +x axis. As the puck slides, a constant acceleration acts on it that has the following components: ax = -0.360 m/s2 and ay = -0.980 m/s2. What is the velocity of the puck at time t = 1.50 s?

2.48 m/s, 13.9° above the +x axis

A tennis ball is struck and departs from the racket horizontally with a speed of 26.8 m/s. The ball hits the court at a horizontal distance of 20.3 m from the racket. How far above the court is the tennis ball when it leaves the racket?

2.812 m

A space vehicle is coasting at a constant velocity of 15.7 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.360 m/s2 in the +x direction. After 46.7 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction.

23.016 m/s; 46. 959 degrees

During the first 18 minutes of a 1.0-hour trip, a car has an average speed of 11 m/s. What must the average speed of the car be during the last 42 minutes of the trip be if the car is to have an average speed of 21 m/s for the entire trip?

25 m/s

A rock, dropped from rest near the surface of an atmosphere-free planet, attains a speed of 20.0 m/s after falling 8.0 meters. What is the magnitude of the acceleration due to gravity on the surface of this planet?

25 m/s2

Suppose a car is traveling at +16.5 m/s, and the driver sees a traffic light turn red. After 0.511 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 7.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

27.88 m

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.35 m/s. The car is a distance d away. The bear is 17.1 m behind the tourist and running at 8.41 m/s. The tourist reaches the car safely. What is the maximum possible value for d?

29.9 m

A boat that can travel at 4.0 km/h in still water crosses a river with a current of 2.0 km/h. At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the river?

30 degrees

A physics student standing on the edge of a cliff throws a stone vertically downward with an initial speed of 10.0 m/s. The instant before the stone hits the ground below, it is traveling at a speed of 30.0 m/s. If the physics student were to throw the rock horizontally outward from the cliff instead, with the same initial speed of 10.0 m/s, what is the magnitude of the velocity of the stone just before it hits the ground?

30.0 m/s

The drawing shows two cars traveling in different directions with different speeds. Their velocities are: vAG = velocity of car A relative to the Ground = 29.5 m/s, due eastvBG = velocity of car B relative to the Ground = 21.0 m/s, due north The driver of car B looks out the window and sees car A. What is the velocity (magnitude and direction) of car A as observed by the driver of car B? In other words, what is the velocityvABof car A relative to car B?

36.13 m/s; 35.4 south of east

Each drawing shows three points along the path of a projectile, one on its way up, one at the top, and one on its way down. The launch point is on the left in each drawing. Which drawing correctly represents the acceleration a of the projectile at these three points?

4

Before working this problem, review Conceptual Example 14. A pellet gun is fired straight downward from the edge of a cliff that is 10.6 m above the ground. The pellet strikes the ground with a speed of 32.7 m/s. How far above the cliff edge would the pellet have gone had the gun been fired straight upward?

43.96 m

A basketball is launched with an initial speed of 8.0 m/s and follows the trajectory shown. The ball enters the basket 0.96 s after it is launched. What are the distances x and y? Note: The drawing is not to scale.

5.4 m; 0.91 m

A person who walks for exercise produces the position-time graph shown. Calculate the average velocity, including sign, for (a) segment A, (b) segment B, (c) segment C, and (d) segment D.

6.25; -3.75; 0.625 km/h; 0.00

One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 1.48 km. They start at the west side of the lake and head due south to begin with. (a) What is the distance they travel? (b) What is the magnitude of the couple's displacement? (c) What is the direction (relative to due east) of the couple's displacement?

6.97 km; 2.09 km; 45 degrees

Two soccer players start from rest, 27 m apart. They run directly toward each other, both players accelerating. The first player's acceleration has a magnitude of 0.50 m/s2. The second player's acceleration has a magnitude of 0.48 m/s2. (a) How much time passes before the players collide? (b) At the instant they collide, how far has the first player run?

7.423 s; 13.775 m

A volleyball is spiked so that it has an initial velocity of 12.9 m/s directed downward at an angle of 52.4 ° below the horizontal. What is the horizontal component of the ball's velocity when the opposing player fields the ball?

7.87 m/s

A police car is traveling at a velocity of 20.0 m/s due north, when a car zooms by at a constant velocity of 44.0 m/s due north. After a reaction time 0.500 s the policeman begins to pursue the speeder with an acceleration of 6.00 m/s^2. Including the reaction time, how long does it take for the police car to catch up with the speeder?

8.972 s

In diving to a depth of 769 m, an elephant seal also moves 318 m due east of his starting point. What is the magnitude of the seal's displacement?

832.16 m

Let's say you are trying to shoot a monkey hanging by his tail in a tree. Assume that when you fire, the monkey gets scared and let's go of the tree so that he falls. Where should you aim?

aim directly at the monkey

A boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. A vector from the station to the point where the boat was later found is B→B→ = 30.0 km, 15.0° north of east. What are the components of the vector from the point where the distress call was made to the point where the boat was found? In other words, what are the components of vector C→C→ = B→B→ - A→A→?

x-component: 17.3 km east, y-component: 35.7 km south

A jogger runs along a straight and level road for a distance of 8.0 km and then runs back to her starting point. The time for this roundtrip is 2.0 h. Which one of the following is true?

Her average speed is 8.0 km/h, and her average velocity is 0 km/h.

Two objects A and B accelerate from rest with the same constant acceleration. Object A accelerates for twice as much time as object B, however. Which one of the following statements is true concerning these objects at the end of their respective periods of acceleration?

Object A will travel four times as far as object B.

Two objects are fired into the air, and the drawing shows the projectile motions. Projectile 1 reaches the greater height, but projectile 2 has the greater range. Which one is in the air for the greater amount of time?

Projectile 1, because it travels higher than projectile 2

A tennis ball is thrown upward at an angle from point A. It follows a parabolic trajectory and hits the ground at point D. At the instant shown, the ball is at point B. Point C represents the highest position of the ball above the ground. Which statement is true concerning the ball when it is at C, the highest point in its trajectory?

The ball's velocity is perpendicular to its acceleration.