Question 1

A boat, whose speed in still water is 8.0 m/s, crosses a river with a current of 6.0 m/s. If the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing
On the shore as it crosses the river?
A) 10.0 m/s
B) 5.3 m/s
C) 6.0 m/s
D) 8.0 m/s

Accepted Answer

The speed of the boat relative to an observer on the shore is the resultant of the boat's speed in still water and the current's speed. This can be found using the Pythagorean theorem since the boat's direction and the current's direction are perpendicular to each other. $ \sqrt{(8.0)^2 + (6.0)^2} = \sqrt{64 + 36} = \sqrt{100} = 10.0 $ m/s.

Question 2

A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0° below the horizontal is applied to the box. The coefficient of static friction between the box and the
Surface is 0.40, and the coefficient of kinetic friction is 0.30. What is the force of friction on the box?
A) 220 N
B) 620 N
C) 250 N
D) 200 N
E) 32 N

Accepted Answer

The force of friction can be calculated using the formula $f = \mu N$, where $f$ is the force of friction, $\mu$ is the coefficient of friction, and $N$ is the normal force. The normal force in this case is the weight of the box minus the vertical component of the applied force. The weight of the box is $mg = 50 \times 9.8 = 490\,N$. The vertical component of the applied force is $250 \sin(30^\circ) = 125\,N$. Thus, the normal force is $490 - 125 = 365\,N$. Using the coefficient of static friction ($\mu_s = 0.40$), the force of friction is $0.40 \times 365 = 146\,N$. However, none of the provided options match this calculation directly, suggesting a misunderstanding in the interpretation of the question or a mistake in the calculation. Given the options, the closest approach to understanding the scenario would involve recognizing a potential error in calculation or interpretation rather than selecting from the provided choices based on the direct calculation. Therefore, the correct response based on the standard approach to calculating frictional force seems absent, indicating a need to reassess the calculation or the interpretation of the question's details.

Question 3

The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes 0.53 s for it to reach the floor. What is the mass m of the block on the left? There is no friction or mass in
The pulley, and the connecting rope is very light.

A)  16 kg
B)  13 kg
C)  14 kg
D)  11 kg

Accepted Answer

The answer of The figure shows a 100-kg block being...

Question 4

A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes
(thereby locking the wheels) and the point where the car came to a stop was 28.0 m. From a
Reference manual he determines that the coefficient of kinetic friction between the tires and the
Road under the prevailing conditions was 0.300. How fast was the car going when the driver
Applied the brakes?
A) 12.8 m/s
B) 21.4 m/s
C) 45.7 m/s
D) 10.7 m/s
E) 32.9 m/s

Accepted Answer

Using the formula for stopping distance: $ v^2 = 2 \mu g d $, where $ \mu = 0.300 $, $ g = 9.8 \, \text{m/s}^2 $, and $ d = 28.0 \, \text{m} $, we find $ v = \sqrt{2 \times 0.300 \times 9.8 \times 28.0} \approx 12.8 \, \text{m/s} $.

Question 5

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current?
A) 1.4 m/s
B) 1.2 m/s
C) 0.50 m/s
D) 0.80 m/s
E) 1.8 m/s

Accepted Answer

The swimmer is swept 480 m downstream in 6 min 40 s (400 seconds). The speed of the current is the distance swept downstream divided by the time, which is 480 m / 400 s = 1.2 m/s.

Question 6

In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When
Block B is gently released from rest, how long does it take block B to travel 80.0 cm? 
A) 0.935 s
B) 0.494 s
C) 0.639 s
D) 0.785 s
E) 0.404 s

Accepted Answer

The answer of In the figure, block A has a...

Question 7

An object slides on a level floor. It slows and comes to a stop with a constant acceleration of magnitude 2.4 m/s². What is the coefficient of kinetic friction between the object and the floor?
A) 0.24
B) 0.12
C) 0.48
D) It is impossible to determine without knowing the mass of the object.

Accepted Answer

The coefficient of kinetic friction is given by the equation:$$f_k = \mu_k * n$$where:* $f_k$ is the force of kinetic friction* $\mu_k$ is the coefficient of kinetic friction* $n$ is the normal forceIn this problem, the normal force is equal to the weight of the object:$$n = mg$$where:* $m$ is the mass of the object* $g$ is the acceleration due to gravityThe force of kinetic friction is equal to the mass of the object times the acceleration:$$f_k = ma$$where:* $a$ is the acceleration of the objectSubstituting these equations into the first equation, we get:$$\mu_k = \frac{ma}{mg} = \frac{a}{g}$$Plugging in the given values, we get:$$\mu_k = \frac{2.4 \ m/s^2}{9.8 \ m/s^2} = 0.24$$Therefore, the coefficient of kinetic friction is 0.24.

Question 8

A bulldozer attempts to drag a log weighing 500 N along the rough horizontal ground.
The cable attached to the log makes an angle of  above the ground. The coefficient of
static friction between the log and the ground is 0.50, and the coefficient of kinetic friction
is 0.35. What minimum tension is required in the cable in order for the log to begin to
slide?

Accepted Answer

The answer of A bulldozer attempts to drag a log...

Question 9

A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is 
A)  157 m/s at an angle  south of east.
B)  155 m/s  at an angle  east of south.
C)  155 m/s  at an angle  south of east.
D)  157 m/s  at an angle  south of east.
E)  157 m/s  at an angle  east of south.

Accepted Answer

The answer of A plane has an eastward heading with...

Question 10

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the point of origin of the flight. The plane flies with an airspeed of 120 m/s. If a
Constant wind blows at 10 m/s toward the west during the flight, what direction must the plane fly
Relative to the air to arrive at the destination? 
A)  west of north
B)  west of north
C)  east of north
D)  west of north
E)  east of north

Accepted Answer

The answer of An airplane flies between two points on...

Question 11

A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the heading of the plane in order to move directly eastward relative To the ground? 
A)  north of east
B)  north of east
C)  north of east
D)  north of east
E)  north of east

Accepted Answer

The answer of A plane has an airspeed of 142...

Question 12

A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box
and the surface is 0.30, and the coefficient of kinetic friction is 0.20. What horizontal force
must be applied to the box to cause it to start sliding along the surface?

Accepted Answer

The answer of A 55-kg box rests on a horizontal...

Question 13

A 960-m wide river flows at 16 m/s as shown in the figure. Alice and John have a race in
identical boats which each travel 20 m/s in still water. Alice leaves point A and steers so
that she goes straight to point B directly across and then back to A. John leaves point A
and steers up to point C (960 m upstream) and then returns to A.
(a) Which person arrives back at point A first?
(b) How much sooner than the loser does the winner arrive back at point A?

Accepted Answer

The answer of A 960-m wide river flows at 16...

Question 14

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3°
(with respect to a line perpendicular to the shore) in order to travel directly across the
stream.
(a) What is the speed of the current?
(b) What is the resultant speed of the boat with respect to the shore?

Accepted Answer

The answer of A boat, whose speed in still water...

Question 15

A 50-kg box is being pushed along a horizontal surface. The coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. What horizontal force
Must be exerted on the box for it to accelerate at 1.2 m/s²?
A) 170 N
B) 120 N
C) 60 N
D) 490 N
E) 230 N

Accepted Answer

To find the force needed to accelerate the box, first calculate the force of kinetic friction: F_friction = μ_k * m * g = 0.35 * 50 kg * 9.8 m/s² = 171.5 N. Then, calculate the net force required for acceleration: F_net = m * a = 50 kg * 1.2 m/s² = 60 N. The total force needed is the sum of the force to overcome friction and the net force: F_total = 171.5 N + 60 N = 231.5 N, which is closest to 230 N.

Question 16

The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30, respectively. What is the force of friction on the box when a 15-N horizontal push is
Applied to the box?
A) 15 N
B) 8.8 N
C) 12 N
D) 4.5 N
E) 6.0 N

Accepted Answer

The force of friction when the box is moving is given by the kinetic friction formula: $f_k = \mu_k N$, where $\mu_k$ is the coefficient of kinetic friction and $N$ is the normal force. The normal force for a horizontal surface is equal to the weight of the object, which is $mg$, where $m = 3.0 \, \text{kg}$ and $g = 9.8 \, \text{m/s}^2$. Therefore, $N = 3.0 \times 9.8 = 29.4 \, \text{N}$. The kinetic friction force is $f_k = 0.30 \times 29.4 = 8.82 \, \text{N}$, which rounds to $8.8 \, \text{N}$, indicating that the box is moving and the kinetic friction force applies.

Question 17

A plane flies directly from city A to city B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The
Trip from B to A takes 65 min less than the trip from A to B. What is the airspeed (assumed
Constant) of the plane relative to the air (that is, the airspeed)?
A) 610 mi/h
B) 400 mi/h
C) 480 mi/h
D) 530 mi/h

Accepted Answer

The answer of A plane flies directly from city A...

Question 18

A plane has an airspeed of  142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity?
A)  48 m/s
B)  130 m/s
C)  16 m/s
D)  141 m/s
E)  160 m/s

Accepted Answer

The magnitude of the velocity of the plane relative to the ground is found by subtracting the wind's velocity vector from the plane's airspeed vector. Since the wind is blowing southward and the plane's ground velocity is directly eastward, the wind's effect is perpendicular to the plane's direction of travel. Using the Pythagorean theorem, $ \sqrt{142^2 - 16^2} = 141 $ m/s, which is the plane's velocity relative to the ground.

Question 19

A locomotive is pulling three train cars along a level track with a force of 100,000 N. The
car next to the locomotive has a mass of 80,000 kg, the next one, 50,000 kg, and the last
one, 70,000 kg. You can neglect the friction on the cars being pulled.
(a) What is the magnitude of the force between that the 80,000-kg car exerts on the
50,000-kg car?
(b) What is the magnitude of the force that the 50,000-kg car exerts on the 70,000-kg car?

Accepted Answer

The answer of A locomotive is pulling three train cars...

Question 20

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water?
A) 1.8 m/s
B) 0.50 m/s
C) 1.2 m/s
D) 0.80 m/s
E) 1.4 m/s

Accepted Answer

The answer of A swimmer heading directly across a river...

Quiz 3: Kinematics in Two Dimensions; Vectors

A boat, whose speed in still water is 8.0 m/s, crosses a river with a current of 6.0 m/s. If the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing On the shore as it crosses the river?

The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes 0.53 s for it to reach the floor. What is the mass m of the block on the left? There is no friction or mass in The pulley, and the connecting rope is very light.

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current?

In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When Block B is gently released from rest, how long does it take block B to travel 80.0 cm?

An object slides on a level floor. It slows and comes to a stop with a constant acceleration of magnitude 2.4 m/s². What is the coefficient of kinetic friction between the object and the floor?

A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is

A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the heading of the plane in order to move directly eastward relative To the ground?

A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30, and the coefficient of kinetic friction is 0.20. What horizontal force must be applied to the box to cause it to start sliding along the surface?

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current? (b) What is the resultant speed of the boat with respect to the shore?

A 50-kg box is being pushed along a horizontal surface. The coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. What horizontal force Must be exerted on the box for it to accelerate at 1.2 m/s²?

The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30, respectively. What is the force of friction on the box when a 15-N horizontal push is Applied to the box?

A plane has an airspeed of 142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity?

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water?