Q: Given two vectors $$\vec{A}$$ and $$\vec{B}$$, which of the following correctly expresses the scalar (dot) product?

$$\vec{A} \cdot \vec{B} = AB \cos \theta$$

Question 1

A ball is dropped from a pole attached to a cart moving at a constant speed to the right. How does the trajectory of the ball appear to an observer on the cart compared to an observer on the ground?

Accepted Answer

To the cart observer, the ball falls straight down; to the ground observer, the ball follows a curved path.

Question 2

Which statement about the magnitude of acceleration of a dropped object, as measured by different observers (one on a moving train, one standing next to the track), is correct?

Accepted Answer

The acceleration is the same for both observers.

Question 3

Is vector addition commutative? Is vector subtraction commutative?

Accepted Answer

Yes, no

Question 4

Given two vectors $$\vec{A}$$ and $$\vec{B}$$, which of the following correctly expresses the scalar (dot) product?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos 	heta$$

Question 5

A suitcase moves at constant velocity up an inclined conveyor belt. Which force component is responsible for keeping the suitcase from accelerating perpendicular to the belt?

Accepted Answer

Normal component

Question 6

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 7

When analyzing the motion of a brick sliding down an inclined plane, which coordinate system is most useful?

Accepted Answer

Axes aligned with the direction of acceleration and perpendicular to it.

Question 8

A friend sits on a swing at rest. You pull the swing to an angle $$	heta$$ and hold it. As $$	heta$$ increases, what happens to the magnitude of the force you must exert to keep the swing in place?

Accepted Answer

It increases.

Question 9

In two-dimensional motion, what effect does the component of acceleration perpendicular to the instantaneous velocity have?

Accepted Answer

It changes the direction of the velocity but not its magnitude.

Question 10

A coffee cup sits on your car dashboard as you accelerate forward. What type of friction keeps the cup from sliding, and does this friction do work on the cup?

Accepted Answer

Static friction; it does positive work.

Question 11

If $$\vec{A} = 4\hat{i} + 3\hat{j}$$ and $$\vec{B} = 2\hat{i} - 5\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$6\hat{i} - 2\hat{j}$$

Question 12

A ball is moving in a plane with velocity $$\vec{v}$$ and acceleration $$\vec{a}. If$$ $$\vec{a} is $$parallel to $$\vec{v}$$, what happens to the ball's speed?

Accepted Answer

It increases.

Question 13

Which of the following is true about the vector difference $$\vec{A} - \vec{B}$$?

Accepted Answer

It is obtained by reversing $$\vec{B}$$ and adding it to $$\vec{A}.$$

Question 14

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the positive x-axis. What is the x-component of $$\vec{A}$$?

Accepted Answer

$$A \cos 	heta$$

Question 15

A force acts on an object moving in a plane. The force has both parallel and perpendicular components to the velocity. What is the effect on the object's motion?

Accepted Answer

Both the speed and direction change.

Question 16

If a vector $$\vec{A}$$ has components $$A_x$$ and $$A_y$$, what is the formula for its magnitude?

Accepted Answer

$$A = \sqrt{A_x^2$ + A_y^2$}$$

Question 17

When pulling a friend on a swing at rest, how does the force exerted by the swing seat compare to the gravitational force as the angle $$	heta$$ increases?

Accepted Answer

It becomes larger than the gravitational force.

Question 18

Which of the following best describes the process of decomposing a vector in a plane?

Accepted Answer

Splitting the vector into two perpendicular components along chosen axes.

Question 19

A ball's instantaneous velocity does not point in the same direction as its displacement. What does this indicate about its motion?

Accepted Answer

The ball's path is curved, and velocity is tangent to the trajectory.

Question 20

When choosing a coordinate system for a problem involving acceleration, what is the recommended strategy?

Accepted Answer

Align one axis with the direction of acceleration.

Chapter 10: Motion in a Plane – Principles & Practice of Physics (Vectors and Forces in Two Dimensions)

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