Physics Chapter 3: Falling Objects and Motion

Constant downward acceleration of objects due to gravity, regardless of their upward or downward motion.

An object moving upward still experiences a downward acceleration due to gravity.

Zero velocity at the highest point of an object's upward trajectory.

Acceleration remains constant at -9.81 m/s² (downwards) even at the peak of the object's trajectory.

Negative acceleration with negative velocity indicates increasing speed downwards

Positive velocity, negative acceleration means the ball's speed is reducing as it rises in the air.

Objects in motion, whether up or down, still experience a constant downward acceleration (due to gravity).

Motion along a straight line, a key concept in Physics to understand motion, including free-fall.

Projectile motion is free fall with an initial horizontal velocity.

The vertical component of a projectile's motion follows free fall kinematics, with constant downward acceleration due to gravity.

Free fall is motion under the influence of gravity alone.

The vertical acceleration of a projectile (on Earth) is always constant and downward, approximately 9.81 m/s².

Projectile motion can be analyzed by separating it into independent horizontal and vertical components. The horizontal component does not affect the vertical.

Vertical and horizontal movements happen at same time.

Air resistance affects the constant projectile motion by causing deceleration.

Despite initial horizontal velocity, the vertical motion of a projectile is unaffected by horizontal component.

The vector that represents the sum of two or more vectors.

Adding vectors by drawing them to scale and using a ruler and protractor.

The length of the vector, representing its size or strength.

The angle a vector makes with a reference line or another vector.

Using a ratio (e.g., 50 m = 1 cm) to represent vector lengths on a diagram.

The starting point of a vector.

The endpoint of a vector.

The change in position of an object or person.

If one component of a vector along the direction of another vector is zero, the two vectors are perpendicular. This means they form a 90-degree angle with each other.

Earth's motion is negligible during the short time a ball is thrown straight up in the air. This means that the ball returns to the same point because of gravity, not the Earth's motion.

A viewpoint or perspective from which motion is observed. It can be stationary or moving.

The velocity of an object as measured by an observer in a different frame of reference.

An object's observed motion can vary depending on the observer's frame of reference.

The velocity of an object moving parallel to the ground (left to right or right to left).

The velocity of an object moving perpendicular to the ground (up or down).

The part of an object's velocity that is parallel to the ground, maintaining its horizontal speed.

The horizontal component of velocity remains constant throughout the projectile's flight when air resistance is negligible.

The vertical displacement of a projectile is calculated using ∆y = 0.5 * ay * (∆t)^2, where ay is the vertical acceleration and ∆t is the time of flight.

The time of flight (∆t) for a projectile launched horizontally can be solved for using the vertical displacement equation as: ∆t = √(2 *|∆y|/|ay|).

The horizontal velocity (vx) can be calculated by rearranging the horizontal displacement equation: vx = ∆x / ∆t.

When calculating velocity, the positive square root should be taken because speed is a positive value.

Estimate the time of flight and then use the acceleration due to gravity to approximate the vertical displacement.

A object moves horizontally and then falls due to the effects of gravity.

Velocity has two components: horizontal (constant) and vertical (affected by gravity).

A scalar is a quantity that has magnitude but no direction. Examples include speed, volume, and mass.

A vector is a quantity that has both magnitude and direction. Examples include displacement, velocity, and acceleration.

Vectors are represented by boldface symbols in physics. For example, the velocity of a bird is written as v = 3.5 m/s.

Speed is a scalar quantity that only tells how fast something is moving. Velocity is a vector quantity that tells both how fast something is moving and in what direction.

Displacement is a vector quantity that describes the change in position from the starting point to the final point of an object.

The constant acceleration experienced by objects in free fall, approximately 9.81 m/s² downwards on Earth. This means velocity increases by 9.81 m/s every second.

A bigger displacement between images of a falling object indicates a faster speed during that interval.

The time interval between an event and your response to it.

You can determine your reaction time by measuring how far a dropped object falls before you catch it, and using the equation for constantly accelerated motion.

Components are the projections of a vector along the axes of a coordinate system. They represent the vector's influence in each direction.

Resolving a vector lets you analyze motion in each direction separately, making it easier to understand complex movements.

The final velocity of an object when multiple velocities act on it.

Combining two or more vectors to find a single resultant vector representing the overall effect. This sum is independent of the order of the addition.

A graphical method for adding vectors where vectors are drawn to scale, head to tail, and the resultant is drawn from the first tail to the last head.

Adding the opposite (negative) of a vector to find the difference between two vectors. The negative has the same magnitude but opposite direction.

A vector with the same magnitude as the original but an opposite direction. Adding a vector and its negative equals zero.

Vectors pointing in opposite directions have a 180-degree angle between them.

Multiplying a vector by a scalar changes its magnitude by the scalar's value. Negative scalars reverse the vector's direction.

Vectors are typically represented by arrows. The length of the arrow represents the magnitude, and the arrowhead points in the direction.

The curved path of a projectile, shaped like a parabola.

Force that opposes the motion of an object through the air, affecting its trajectory.

The horizontal speed of a projectile remains the same throughout its flight, neglecting air resistance.

The constant downwards acceleration that affects the vertical component of a projectile's motion.

The slope of a velocity-time graph represents the acceleration of the object. A steeper slope means a greater acceleration.

Objects in free fall experience a constant acceleration due to gravity, indicated by a consistent increase in velocity over time.

The acceleration of an object in free fall remains constant at approximately -9.81 m/s², regardless of its upward or downward motion.

When an object reaches its highest point in free fall, its velocity momentarily becomes zero.

Regardless of their mass, objects in free fall experience the same acceleration due to gravity, resulting in equal displacement over the same time.

Even at the highest point, the acceleration of an object in free fall remains constant at -9.81 m/s².

Even when an object moves upwards, it still experiences a constant downward acceleration due to gravity.

A positive velocity with negative acceleration means the object is slowing down as it moves upwards.

A negative velocity with negative acceleration means the object is speeding up as it moves downwards.

When an object is slowing down, its velocity and acceleration have opposite signs. If velocity is positive, acceleration is negative, and vice versa.

The mass of an object does not affect its acceleration in free fall. All objects fall at the same rate regardless of their weight.

You can determine the acceleration of an object from a velocity-time graph by calculating the slope of the line. A constant slope indicates constant acceleration.

Projectile motion is free fall with an additional initial horizontal velocity, causing it to follow a curved path.

The horizontal and vertical components of the initial velocity of a projectile, found using sine and cosine.

The part of a projectile's velocity that remains constant throughout its flight, unaffected by gravity.

The part of a projectile's velocity affected by gravity, changing constantly throughout the flight.

Only gravity affects the vertical motion of a projectile, not the horizontal component of its velocity.

The horizontal component of velocity remains constant throughout a projectile's flight, neglecting air resistance.

A projectile's path, due to gravity, follows a curved trajectory, often described as a parabola.

Analyze projectile motion by separating it into independent horizontal and vertical components, each obeying its own set of rules. This makes calculating the motion easier.

To subtract a vector, add its opposite. The opposite has the same magnitude but points in the opposite direction.

The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

The cosine of an angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

It's the horizontal velocity of the plane, which is the velocity the truck needs to maintain to stay beneath it.

Trigonometry allows us to break down the plane's velocity into its horizontal and vertical components, using sine and cosine functions.

The truck's velocity must be equal to the x-component of the plane's velocity for the truck to stay beneath the plane.

You can use the cosine function: vx = vplane * cos(angle), where vx is the x-component, vplane is the plane's velocity, and angle is the angle of the plane's velocity relative to the ground.

The hypotenuse represents the plane's total velocity, which is the vector sum of its horizontal and vertical components.

A steeper angle means a smaller x-component, requiring the truck to move slower. A shallower angle means a larger x-component, requiring the truck to move faster.

The part of an object's velocity that's affected by gravity during projectile motion. It's the movement up and down.

Because the airplane and the dummy have the same horizontal velocity. The dummy falls straight down relative to the airplane, but the airplane's forward motion means the dummy stays aligned with the plane.

A ball thrown straight up is a special case of projectile motion with an initial horizontal velocity of zero. The ball still experiences gravity's influence.

A frame of reference is a perspective or viewpoint from which motion is observed. An example is a passenger on a train observing a ball being thrown.

The part of a projectile's velocity that remains constant throughout its flight, unaffected by gravity. It's the speed in the sideways direction.

The part of a projectile's velocity that changes due to gravity, constantly increasing downwards. It's the speed in the up-and-down direction.

Analyzing projectile motion involves separating its motion into independent horizontal and vertical components, each following their own set of rules.

Resolving vectors into components makes analyzing motion easier by allowing us to study movement in each direction separately.

Gravity affects the vertical velocity of a projectile, constantly increasing its downwards speed. This causes the curved trajectory.

Using x and y components to describe motion avoids vector multiplication, making calculations of displacement, velocity, and acceleration more straightforward.

A physical quantity with magnitude but no direction, like speed or volume.

A physical quantity with both magnitude and direction, like displacement or velocity.

A single vector that represents the combined effect of two or more vectors acting on an object.

Vectors are drawn tail-to-head to scale, forming a triangle or polygon, with the resultant drawn from the first tail to the last head.

A vector with the same magnitude but opposite direction; used when subtracting vectors.

Multiplying a vector by a scalar changes its magnitude, while a negative scalar reverses its direction.

The perspective or viewpoint from which motion is observed; can be stationary or moving.

The velocity of an object as measured by an observer in a different frame of reference.

In projectile motion, if air resistance is negligible, there's no horizontal force acting on the object to slow it down or speed it up, so the horizontal velocity stays the same.

A projectile's path, due to gravity, follows a curved trajectory, often described as a parabola.

The vertical component of a projectile's velocity is influenced by gravity—a constant downward acceleration of approximately 9.81 m/s². This means the object speeds up as it falls.

The time of flight is the total time a projectile spends in the air. It's determined by the projectile's initial vertical velocity and the acceleration due to gravity.

Horizontal displacement is the horizontal distance a projectile travels during its motion. It's determined by the projectile's horizontal velocity and the time of flight.

Vertical displacement is the vertical distance a projectile travels during its motion. It's determined by the projectile's initial vertical velocity, the acceleration due to gravity, and the time of flight.

Neglecting air resistance simplifies projectile motion analysis. This means ignoring the force of air that slows down the projectile, making it easier to calculate the motion.

The constant sideways speed of a projectile. It doesn't change due to gravity.

The speed of a projectile going up or down. It's affected by gravity.

The angle at which a projectile is launched, determining the shape of its trajectory.

The projectile's speed and direction at the start of its motion.

The total time a projectile stays in the air, from launch to landing.

The horizontal distance a projectile travels. How far it goes sideways.

The speed of the spy as seen by the observer on the submarine is the vector sum of the spy's velocity relative to the carrier and the carrier's velocity relative to the submarine.

Since the ferry moves north and the river flows east, its velocity relative to Earth is the vector sum of both velocities, forming a right triangle.

The dog's velocity is the vector sum of its velocity relative to the truck and the truck's velocity relative to the road.

The boy appears to be moving faster to the woman because their velocities are in opposite directions. You add the magnitudes of the two velocities.

The ball's velocity relative to the ground is the vector sum of its velocity relative to the walkway and the walkway's velocity relative to the ground.