Chapter 2: Two-Dimensional Kinematics - Review Questions

What is the shortest distance between two points in a two-dimensional motion scenario?

a) The sum of the horizontal and vertical distances

b) The straight-line path

c) The path taken by the object

d) The average of the horizontal and vertical distances

b) The straight-line path

Which theorem is used to calculate the straight-line distance in a right triangle formed by two-dimensional motion?

a) Pythagorean Theorem

b) Newton's First Law

c) Law of Sines

d) Law of Cosines

a) Pythagorean Theorem

What does the independence of perpendicular motions imply in two-dimensional motion?

a) Horizontal motion affects vertical motion

b) Vertical motion affects horizontal motion

c) Horizontal and vertical motions are independent

d) Both motions are dependent on each other

c) Horizontal and vertical motions are independent

In projectile motion, what are the two independent components of motion?

a) Horizontal and vertical

b) Circular and elliptical

c) Linear and rotational

d) Diagonal and parallel

a) Horizontal and vertical

The Pythagorean theorem is used to calculate the ___ distance in a right triangle formed by two-dimensional motion.

straight-line

What happens to a vector when it is multiplied by a negative scalar?

a) Its magnitude increases and direction remains the same

b) Its magnitude decreases and direction remains the same

c) Its magnitude remains the same and direction reverses

d) Its magnitude changes and direction reverses

d) Its magnitude changes and direction reverses

What is the result of subtracting vector B from vector A?

a) A + B

b) A - B

c) A + (-B)

d) A - (-B)

c) A + (-B)

Which of the following is true about vector addition?

a) Vector addition is commutative

b) Vector addition is associative

c) Vector addition is neither commutative nor associative

d) Vector addition is both commutative and associative

d) Vector addition is both commutative and associative

The head-to-tail method involves placing the tail of the second vector at the ___ of the first vector.

head

The negative of a vector has the same magnitude but the opposite ___.

direction

Explain how to graphically subtract vector B from vector A.

To graphically subtract vector B from vector A, first reverse the direction of vector B to get -B. Then, add -B to vector A using the head-to-tail method.

What is the primary advantage of using analytical methods over graphical methods for vector addition and subtraction?

a) Greater accuracy and precision

b) Easier visualization

c) Requires less mathematical knowledge

d) Faster computation

a) Greater accuracy and precision

Which equation is used to find the x-component of a vector given its magnitude and angle?

a) Ax = A cos θ

b) Ax = A sin θ

c) Ax = A tan θ

d) Ax = A / cos θ

a) Ax = A cos θ

How do you calculate the magnitude of a resultant vector from its components?

a) A = Ax + Ay

b) A = Ax^2 + Ay^2

c) A = sqrt(Ax^2 + Ay^2)

d) A = Ax * Ay

c) A = sqrt(Ax^2 + Ay^2)

What is the formula to find the direction of a vector from its components?

a) θ = sin^(-1)(Ay/A)

b) θ = cos^(-1)(Ax/A)

c) θ = tan^(-1)(Ay/Ax)

d) θ = tan^(-1)(Ax/Ay)

c) θ = tan^(-1)(Ay/Ax)

The equation to find the y-component of a vector is Ay = ___ θ.

A sin

To find the magnitude of a vector from its components, use the equation A = ___(Ax^2 + Ay^2).

sqrt

Explain why analytical methods are preferred over graphical methods for vector addition and subtraction in physics.

Analytical methods are preferred because they provide greater accuracy and precision, as they rely on mathematical calculations rather than the limitations of drawing accuracy.

Which of the following is true about the vertical motion of a projectile?

a) It is independent of horizontal motion.

b) It is affected by horizontal velocity.

c) It is constant throughout the trajectory.

d) It is unaffected by gravity.

a) It is independent of horizontal motion.

What is the maximum range of a projectile on level ground achieved at?

a) 30°

b) 45°

c) 60°

d) 90°

b) 45°

The path followed by a projectile is called its ___.

trajectory

The horizontal component of a projectile's velocity is given by v_x = v_0 cos ___.

theta

The vertical component of acceleration for a projectile is a_y = ___.

-9.8 m/s²

Explain why the horizontal and vertical motions of a projectile are independent.

The horizontal and vertical motions of a projectile are independent because they occur along perpendicular axes and are influenced by different factors. The horizontal motion is constant due to the absence of horizontal forces (assuming no air resistance), while the vertical motion is affected by gravity, causing it to accelerate downward.

What is the velocity of an object relative to an observer?

a) The sum of the object's velocity and the observer's velocity

b) The difference between the object's velocity and the observer's velocity

c) The object's velocity relative to the medium

d) The observer's velocity relative to the medium

a) The sum of the object's velocity and the observer's velocity

Which equation is used to find the magnitude of a velocity vector given its components?

a) v = vx + vy

b) v = vx^2 + vy^2

c) v = sqrt(vx^2 + vy^2)

d) v = vx * vy

c) v = sqrt(vx^2 + vy^2)

What is the significance of the observer in measuring velocity?

a) The observer's velocity is always zero.

b) The observer's frame of reference affects the measured velocity.

c) The observer's velocity is added to the object's velocity.

d) The observer's velocity is subtracted from the object's velocity.

b) The observer's frame of reference affects the measured velocity.

In the context of classical relativity, what is the maximum speed considered?

a) Speed of sound

b) Speed of light

c) 1% of the speed of light

d) 10% of the speed of light

c) 1% of the speed of light

The velocity of an object relative to an observer is the sum of the object's velocity relative to a medium and the medium's velocity relative to the ___.

observer

What is classical relativity and how does it differ from modern relativity?

Classical relativity, first discussed by Galileo and Newton, deals with relative velocities at speeds less than 1% of the speed of light. It assumes that time and space are absolute. Modern relativity, developed by Einstein, includes effects at speeds close to the speed of light and shows that time and space are relative.