Physics Chapter 3: Falling Objects and Motion

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Questions and Answers

Which of the following correctly defines a scalar quantity?

A quantity that only considers direction

A quantity that can be visualized as an arrow

A quantity that has magnitude but no direction (correct)

A quantity with both magnitude and direction

What is a characteristic of vectors compared to scalars?

Vectors represent physical quantities that only have magnitude

Vectors can be added using only numerical values

Vectors require both magnitude and direction to be fully described (correct)

Vectors cannot be multiplied by scalars

Which of the following is an example of a vector quantity?

Mass

Temperature

Area

Velocity (correct)

In which scenario is a scalar quantity most appropriately used?

Measuring wind speed without considering direction Signup and view all the answers

How are vector quantities typically represented in physics?

By boldface symbols to distinguish from scalars Signup and view all the answers

When describing the velocity of an object, which elements must be specified?

Both the speed of the object and the direction of travel Signup and view all the answers

Which of the following statements is false about scalars and vectors?

Scalars can express direction in terms of compass points Signup and view all the answers

Which scenario best illustrates the importance of understanding vector quantities?

Planning a flight path that requires direction and distance Signup and view all the answers

What is the relative speed of the spy when viewed from a stationary submarine if the aircraft carrier is moving forward at 18.0 m/s?

18.0 m/s Signup and view all the answers

What is the primary benefit of resolving vectors into components in projectile motion?

It makes the equations of motion easier to apply separately. Signup and view all the answers

If a ferry moves 2.5 m/s due north while the river flows at 3.0 m/s to the east, what is the resultant velocity of the ferry relative to Earth?

3.60 m/s at 53.13° north of east Signup and view all the answers

What is the velocity of the dog moving at 1.75 m/s at 35.0° east of north relative to a truck moving at 25.0 m/s north?

26.75 m/s at 64.87° north of east Signup and view all the answers

Which of the following statements regarding the components of velocity in projectile motion is true?

Each component can be analyzed using separate equations of motion. Signup and view all the answers

Why are kinematic equations in their vector forms considered difficult to solve for projectile motion?

The displacement, velocity, and acceleration do not point in the same direction. Signup and view all the answers

How fast does the boy appear to move relative to the woman if the woman travels at 9 m/s and the boy moves at 1 m/s in the opposite direction?

10 m/s Signup and view all the answers

What is the velocity of the ball rolled north by a girl on a walkway moving east, with the ball's speed on the walkway at 0.15 m/s and walkway speed at 1.50 m/s?

1.53 m/s at 11.3° north of east Signup and view all the answers

When analyzing a long jumper's motion, which axis represents their horizontal movement during the run-up?

The x-axis for horizontal motion. Signup and view all the answers

From which reference frame would a ball dropped by a boy walking at 1 m/s appear to be moving differently?

From the boy's perspective Signup and view all the answers

During the flight of a projectile, how can the resultant velocity be determined?

By combining the vertical and horizontal components at any point in time. Signup and view all the answers

Which equation best describes the relationship of displacement in one-dimensional projectile motion?

$d = v_i t + \frac{1}{2} a t^2$ Signup and view all the answers

How far does a roller coaster moving at a 40.0° angle cover horizontally if it travels 41.1 m along the slope?

31.5 m Signup and view all the answers

What must be true for a long jumper’s velocity vector while in the air?

Both the horizontal and vertical components vary independently. Signup and view all the answers

What direction will a stationary observer see the roller coaster moving if it's traveling at a 40.0° angle upwards from the horizontal?

Northeast Signup and view all the answers

What is a drawback of using only vector forms of kinematic equations for projectile motion analysis?

They can lead to inaccuracies due to their complexity. Signup and view all the answers

What is the formula used to calculate horizontal distance for a projectile when air resistance is neglected?

$ ext{Δx} = v_x ext{Δt}$ Signup and view all the answers

Which statement is true regarding the vertical motion of a projectile in the absence of air resistance?

The vertical displacement can be negative. Signup and view all the answers

How is the time interval $ ext{Δt}$ for horizontal and vertical movement related in projectile motion?

It is the same for both horizontal and vertical displacements. Signup and view all the answers

What value must be used for $a_y$ in calculations for a projectile in free fall?

$-9.81 ext{ m/s}^2$ Signup and view all the answers

When calculating $v_x$, why is the positive root used?

Only speeds are relevant, direction does not matter. Signup and view all the answers

What is the approximate time interval $ ext{Δt}$ calculated for a horizontal distance of $45 ext{ m}$ with a horizontal velocity around $5.5 ext{ m/s}$?

$8 ext{ s}$ Signup and view all the answers

How can $ ext{Δy}$ be calculated if the time interval and vertical acceleration are known?

$ ext{Δy} = rac{1}{2} a_y ( ext{Δt})^2$ Signup and view all the answers

What does the negative value of $ ext{Δy}$ indicate in the context of projectile motion?

The projectile descends below the initial launch height. Signup and view all the answers

What does the equation $vy,f = ay ∆t$ represent in the context of projectile motion?

The final vertical velocity of the object Signup and view all the answers

Which statement accurately describes the horizontal motion of the launched yellow ball?

The horizontal velocity remains constant throughout the flight. Signup and view all the answers

How is the vertical motion of the launched yellow ball characterized?

It is in free fall like a ball dropped directly down. Signup and view all the answers

What is the significance of the equation $∆y = -rac{1}{2}ay (∆t)^2$ in projectile motion?

It figures out the vertical displacement at any time interval. Signup and view all the answers

To find the total velocity of a projectile during its flight, which method should be used?

Use the Pythagorean theorem for magnitude and tangent for direction. Signup and view all the answers

Which factor does NOT influence the horizontal motion of a projectile, assuming negligible air resistance?

Horizontal acceleration Signup and view all the answers

What happens to the yellow ball and a ball dropped straight down when released at the same time?

They both hit the ground simultaneously. Signup and view all the answers

What does the equation $vx = vx,i = constant$ imply about the horizontal motion of a projectile?

The horizontal velocity is constant throughout the flight. Signup and view all the answers

What is the vertical component of the projectile's initial velocity if launched at an angle $ heta$ with a speed of $50.0 m/s$?

$50.0 sin heta$ Signup and view all the answers

In projectile motion, which equation represents the change in vertical displacement?

$ riangle y = (vi sin heta) riangle t + rac{1}{2} a ( riangle t)^2$ Signup and view all the answers

If the zookeeper kneels $10.0 m$ away from the light pole, what is the horizontal distance traveled by the dart when it reaches the height of the monkey?

$10.0 m$ Signup and view all the answers

What is the height the dart must reach when it travels horizontally towards the monkey?

$4.0 m$ Signup and view all the answers

Which of the following equations allows you to calculate the final vertical velocity of the dart?

$vy,f = vi sin heta + ay riangle t$ Signup and view all the answers

If the angle $ heta$ is increased, what effect does this have on the horizontal distance the projectile can cover?

The distance may decrease or increase based on optimal angle. Signup and view all the answers

Which component of motion is constant for a projectile launched from the zookeeper's gun?

Acceleration due to gravity Signup and view all the answers

What happens to the trajectory of the projectile if it is launched horizontally from the same height?

It will fall freely due to gravity. Signup and view all the answers

Study Notes

Section 3: Falling Objects

Freely falling objects experience constant acceleration due to gravity
This acceleration is approximately 9.81 m/s² on Earth
Objects fall at the same rate regardless of mass (disregarding air resistance)
Demonstrated by David Scott's moon experiment in 1971
Free fall is the motion of an object where gravity is the only force acting

Free Fall

Free fall occurs when only gravity acts on a body
In this state, the body accelerates constantly

Acceleration During Upward and Downward Motion

Objects thrown upwards or downwards have constant downward acceleration
The acceleration remains constant throughout the motion, despite changing direction or velocity.
Velocity changes over time, but acceleration does not at any point.

Vectors and Scalars

Scalars have magnitude only (e.g., speed, time, mass).
Vectors have magnitude and direction (e.g., velocity, displacement, acceleration).
Vectors are often represented by boldfaced symbols.
Vectors can be resolved into components parallel to coordinate axes.

Adding Vectors Graphically

To add vectors graphically, use a scale diagram
Place the tail of the second vector at the tip of the first.
The resultant vector runs from the tail of the first to the tip of the second (in diagram).

Resolving Vectors into Components

Vectors can be broken down into components (x and y)
Components are parallel to the coordinate axes.
The sine and cosine functions can be used to determine components when given angle and vector magnitude.

Projectile Motion

Projectile motion follows a parabolic path due to constant downward acceleration from gravity.
The horizontal and vertical motions are independent.
Horizontal velocity remains constant (if air resistance is disregarded).
Vertical motion is governed by the kinematic equations and a constant downward acceleration.

Vertical Motion of a Projectile

Vertical motion is under constant acceleration.
Equations of motion for vertical component apply.

Horizontal Motion of a Projectile

Horizontal motion remains constant at initial horizontal velocity.
Horizontal component of velocity remains unchanged throughout trajectory.

Projectile Motion Launched Horizontally / At an Angle

Launched objects generally follow a parabolic path due to gravity.
Components of velocity can be used in kinematic calculations for motion in either one dimension.
The kinematic equations from the chapter "Motion in one dimension" can be applied for vertical and horizontal motion separately
Using trigonometry and kinematic equations to analyze vertical and horizontal components independently.

Relative Motion

A frame of reference is the perspective from which we observe motion: either (1) stationary (earth), or frame-of-reference (2) moving with objects
Velocity relative to a frame of reference is affected by one's own movement relative to that point in spacetime
Observers in different frames of reference will often measure different velocities.

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Description

Explore the principles of falling objects and free fall as dictated by gravity in this quiz. Understand the differences between scalars and vectors and how acceleration plays a key role in upward and downward motion. Test your knowledge with key concepts introduced in this chapter.