Question 1

You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

Accepted Answer

To counteract the southward current and reach directly west, you should head in a northwesterly direction. This will allow the current to push you south while your boat's velocity component westward takes you directly across.

Question 2

The components of vectors  and  are as follows:  (1, -1) and  (2, 4). The components of the resultant vector  -  are given by

Accepted Answer

The answer of The components of vectors  and ...

Question 3

The components of vectors  and  are as follows:  = (1, -1) and  = (2, 4). The components of the resultant vector  +  are given by

Accepted Answer

The answer of The components of vectors  and ...

Question 4

Vector  has a magnitude of 16.0 m and is pointing eastward. It is rotated 110.0° clockwise. The component of this vector along west is

Accepted Answer

Since vector 11ea6ebb_72c8_7165_9d78_454e0472d6a6_TB6213_11 is originally pointing eastward, the component of the vector along the west must be in the opposite direction.

To find the component of the vector along the west, we need to use trigonometry. We know the magnitude of the vector (16.0 m) and the angle it makes with the positive x-axis after rotation (110.0° clockwise).

The component of the vector along the west can be found using the following formula:

component along west = magnitude of vector * cos(angle)

component along west = 16.0 * cos(110.0°)

component along west = 5.47 m

Therefore, the answer is B: 5.47 m.

Question 5

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector ?

Accepted Answer

The magnitude of a vector can be found using the Pythagorean theorem: 
|v| = sqrt((v_x)^2 + (v_y)^2) 
Plugging in the given components: 
|11ea6ebb_72c7_fc31_9d78_c7ced595f6f6_TB6213_11| = sqrt((12 m)^2 + (5.0 m)^2) 
= sqrt(144 m^2 + 25 m^2) 
= sqrt(169 m^2) 
= 13 m

Question 6

Vector  has a magnitude of 16.0 m and is pointing eastward. It is rotated counterclockwise by an angle of 110.0°. The component of this vector along west is

Accepted Answer

First, we need to find the horizontal component of the vector after it has been rotated counterclockwise by 110.0°.

Using sine and cosine functions, we can find that the horizontal component of the vector is:

cos(110.0°) x 16.0 m = -5.47 m

Since the vector is pointing eastward and we want the component along west, we take the absolute value of the horizontal component to get:

| -5.47 m | = 5.47 m

Therefore, the component of Vector 11ea6ebb_72c8_9876_9d78_492e7f6e4963_TB6213_11 along west is 5.47 m. The answer is (A).

Question 7

Vector  is 5.5 cm long and points along the x-axis. Vector  is 7.5 cm long and points at +30° above the negative x-axis.
(a) Determine the x- and y-components of Vector  .
(b) Determine the x- and y-components of Vector  (c) Determine the sum of these two vectors in terms of components.
(d) Determine the sum of these two vectors in terms of magnitude and direction.

Accepted Answer

The answer of Vector  is 5.5 cm long and...

Question 8

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) Determine the speed of the current.
(b) Determine the resultant speed of the boat with respect to the shore.

Accepted Answer

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

Question 9

Vector  = 4.00 m points eastward and vector  = 3.00 m points southward. The resultant vector  +  is given by

Accepted Answer

The answer of Vector  = 4.00 m points eastward...

Question 10

A car travels along eastward with a constant velocity. The magnitude of the acceleration of the car is

Accepted Answer

Since the car is moving with a constant velocity, its acceleration is zero. This means that it is not accelerating in any direction, including its speed or direction of motion. Therefore, the correct answer is D) zero.

Question 11

Under which of the following conditions would a car have a westward acceleration?

Accepted Answer

A car traveling eastward with decreasing velocity is experiencing acceleration in the opposite direction, which is westward.

Question 12

If the acceleration of an object is always directed perpendicular to its velocity, then

Accepted Answer

If the acceleration is always perpendicular to the velocity, then the object is changing direction and therefore turning. The magnitude of the velocity may remain constant, but the direction is changing, which means the object is turning.

Question 13

If the acceleration vector of an object is directed parallel to the velocity vector, then

Accepted Answer

When the acceleration vector is parallel to the velocity vector, it means the object is speeding up in the direction of the velocity.

Question 14

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

Accepted Answer

The horizontal component of velocity is found using the formula: v_x = v * cos(θ). Here, v = 20.0 m/s and θ = 25.0°. So, v_x = 20.0 * cos(25.0°) ≈ 18.1 m/s.

Question 15

If the acceleration vector of an object is directed anti-parallel to the velocity vector, then

Accepted Answer

The acceleration vector and velocity vector are anti-parallel, which means they are pointing in opposite directions. This implies that the object is experiencing a deceleration or is slowing down. If the acceleration vector were parallel to the velocity vector, then the object would be speeding up, and if the acceleration were perpendicular to the velocity vector, then the object would be turning.

Question 16

Vector  = 4.00 m points eastward and vector  = 3.00 m points northward. The resultant vector  +  is given by

Accepted Answer

The answer of Vector  = 4.00 m points eastward...

Question 17

Vector  = 4.0 m points eastward and vector  = 3.0 m points westward. The resultant vector  +  is given by

Accepted Answer

The resultant vector is found by adding the two given vectors: 
11ea6ebb_72c9_82e1_9d78_fda7fe415da9_TB6213_11 + 11ea6ebb_72c9_a9f2_9d78_610fcc828009_TB6213_11

Since the first vector is pointing east and the second vector is pointing west, they act in opposite directions. Thus, we subtract the magnitudes of the two vectors to get the magnitude of the resultant vector:

Magnitude of resultant vector = 4.0 m - 3.0 m = 1.0 m

Since the vector pointing east has a larger magnitude than the vector pointing west, the resultant vector still points in the eastward direction. Therefore, the answer is choice C) 1.0 m east.

Question 18

A vector is located in the x-y plane. The x- and y-components of this vector are 4.00 m and 3.00 m, respectively. Find the angle that this vector makes with the positive y-axis.

Accepted Answer

We can use the definition of tangent to find the angle:

$$	an	heta = \frac{	ext{opposite}}{	ext{adjacent}} = \frac{4.00	ext{ m}}{3.00	ext{ m}}$$

Taking the arctangent of both sides of the equation, we get:

$$	heta = \arctan\left(\frac{4.00	ext{ m}}{3.00	ext{ m}}ight) \approx 53.1^\circ$$

Therefore, the answer is choice A) 53.1°.

Question 19

Vector  is 75.0 cm long and points at 30° above the positive x-axis. Vector  is 25.0 cm long and points along the negative x-axis. Vector  is 40.0 cm long and points at 45° below the negative x-axis.
(a) Determine the x- and y-components of Vector  .
(b) Determine the x- and y-components of Vector  .
(c) Determine the x- and y-components of Vector  .
(d) Determine the sum of these three vectors in terms of components.
(e) Determine the sum of these three vectors in terms of magnitude and direction.

Accepted Answer

The answer of Vector  is 75.0 cm long and...

Question 20

A vector has components A_x = 12.0 m and A_y= 5.00 m. What is the angle that vector makes with the x-axis?

Accepted Answer

We can use the formula for the angle between a vector and the x-axis: θ = tan^(-1)(A_y / A_x) θ = tan^(-1)(5.00 m / 12.0 m) θ = 22.6° Therefore, the answer is choice B.

Quiz 3: Vectors in Physics

You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

The components of vectors and are as follows: (1, -1) and (2, 4) . The components of the resultant vector - are given by

The components of vectors and are as follows: = (1, -1) and = (2, 4) . The components of the resultant vector + are given by

Vector has a magnitude of 16.0 m and is pointing eastward. It is rotated 110.0° clockwise. The component of this vector along west is

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector ?

Vector has a magnitude of 16.0 m and is pointing eastward. It is rotated counterclockwise by an angle of 110.0°. The component of this vector along west is

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) Determine the speed of the current. (b) Determine the resultant speed of the boat with respect to the shore.

Vector = 4.00 m points eastward and vector = 3.00 m points southward. The resultant vector + is given by

A car travels along eastward with a constant velocity. The magnitude of the acceleration of the car is

Under which of the following conditions would a car have a westward acceleration?

If the acceleration of an object is always directed perpendicular to its velocity, then

If the acceleration vector of an object is directed parallel to the velocity vector, then

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

If the acceleration vector of an object is directed anti-parallel to the velocity vector, then

Vector = 4.00 m points eastward and vector = 3.00 m points northward. The resultant vector + is given by

Vector = 4.0 m points eastward and vector = 3.0 m points westward. The resultant vector + is given by

A vector is located in the x-y plane. The x- and y-components of this vector are 4.00 m and 3.00 m, respectively. Find the angle that this vector makes with the positive y-axis.

A vector has components A_x = 12.0 m and A_y= 5.00 m. What is the angle that vector makes with the x-axis?

Quiz 3: Vectors in Physics

You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

The components of vectors and are as follows: (1, -1) and (2, 4) . The components of the resultant vector - are given by

The components of vectors and are as follows: = (1, -1) and = (2, 4) . The components of the resultant vector + are given by

Vector has a magnitude of 16.0 m and is pointing eastward. It is rotated 110.0° clockwise. The component of this vector along west is

A vector has components Ax = 12 m and Ay = 5.0 m. What is the magnitude of vector ?

Vector has a magnitude of 16.0 m and is pointing eastward. It is rotated counterclockwise by an angle of 110.0°. The component of this vector along west is

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) Determine the speed of the current. (b) Determine the resultant speed of the boat with respect to the shore.

Vector = 4.00 m points eastward and vector = 3.00 m points southward. The resultant vector + is given by

A car travels along eastward with a constant velocity. The magnitude of the acceleration of the car is

Under which of the following conditions would a car have a westward acceleration?

If the acceleration of an object is always directed perpendicular to its velocity, then

If the acceleration vector of an object is directed parallel to the velocity vector, then

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

If the acceleration vector of an object is directed anti-parallel to the velocity vector, then

Vector = 4.00 m points eastward and vector = 3.00 m points northward. The resultant vector + is given by

Vector = 4.0 m points eastward and vector = 3.0 m points westward. The resultant vector + is given by

A vector is located in the x-y plane. The x- and y-components of this vector are 4.00 m and 3.00 m, respectively. Find the angle that this vector makes with the positive y-axis.

A vector has components Ax = 12.0 m and Ay= 5.00 m. What is the angle that vector makes with the x-axis?

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector ?

A vector has components A_x = 12.0 m and A_y= 5.00 m. What is the angle that vector makes with the x-axis?