p.6
Newton's Laws of Motion
What does it mean if an object is moving with a constant velocity?
C. It is not experiencing a net force in that direction.
p.2
Inclined Plane Definition
What is an inclined plane?
A flat surface at an angle to the horizontal.
p.18
Vertical and Horizontal Motion of Projectiles
How long does it take for the arrow shot horizontally from a 40 m high cliff to reach the ground?
Using the formula t = √(2h/g), where h = 40 m and g = 9.81 m/s², the time is approximately 2.86 seconds.
p.14
Projectile Motion Basics
How is the launch angle θ related to the horizontal and vertical components?
Using the relation tan(θ) = v_y / v_x.
p.14
Projectile Motion Basics
What are the horizontal and vertical components of the rugby ball's velocity?
u_x = 12 m/s and u_y = 15 m/s.
p.13
Vertical and Horizontal Motion of Projectiles
How can we link the vertical and horizontal motion of a projectile?
By using time to connect both components.
p.15
Projectile Motion Basics
If ball A is thrown with an initial velocity of 6 m/s and ball B with 8 m/s, but both have the same initial vertical speed, which will hit the ground first?
Both balls will hit the ground at the same time.
p.19
Projectile Motion Basics
What is a hypothesis for the experiment on launch angle and projectile range?
The range of a projectile will vary with different launch angles, reaching a maximum at 45 degrees.
p.19
Vertical and Horizontal Motion of Projectiles
How do you calculate the angle to the horizontal at which the ball hits the floor?
Angle = arctan(vertical velocity / horizontal velocity).
p.18
Projectile Motion Basics
What is the initial vertical velocity of the bottle rocket launched at an angle of 80° with a maximum height of 49 m?
The initial vertical velocity can be calculated using the formula: v_y = √(2gh), where g = 9.81 m/s² and h = 49 m. Thus, v_y ≈ 9.9 m/s.
p.16
Effects of Air Resistance on Projectiles
How does air resistance affect the maximum height of a projectile?
It reduces the maximum height.
p.10
Projectile Motion Basics
What force acts on a projectile in VCE Physics when air resistance is ignored?
The force due to gravity.
p.18
Projectile Motion Basics
What is the range of the bottle rocket if its horizontal velocity is 5.47 m/s?
The range can be calculated using the formula: range = horizontal velocity × time of flight. Time of flight can be found using the vertical motion equations.
p.9
Projectile Motion Basics
What is a projectile?
An object that has been launched or dropped without any form of self propulsion.
p.11
Projectile Motion Basics
What misconception is addressed regarding falling objects?
'Heavier objects always fall quicker than lighter objects.'
p.8
Newton's Laws of Motion
What is the action force in relation to the normal force acting on the ball?
The weight of the ball acting downwards.
What is the time it takes for the ball to reach the bottom of the hill?
To be calculated without using displacement.
p.13
Projectile Motion Basics
What causes the parabolic arc of a projectile's motion?
Vertical acceleration due to gravity and constant horizontal velocity.
p.14
Projectile Motion Basics
What kinematic equations are used to calculate the time for projectile motion?
Appropriate kinematic equations based on the direction of motion.
p.7
Forces on Inclined Planes
At which point does Garrett have the greatest normal force acting on him?
It depends on the angle of the inclined planes at points P, Q, and R.
p.17
Vertical and Horizontal Motion of Projectiles
Does the ball make it over the net? Show your calculations.
To find the height of the ball when it reaches the net, use s_y = u_y t + 1/2 a t². Here, u_y = 6.43 m/s, t ≈ 1.04 s, and a = -9.8 m/s² (gravity). Calculating gives s_y = 6.43 * 1.04 + 0.5 * (-9.8) * (1.04)² ≈ 3.35 m. Since 3.35 m > 1.0 m, the ball makes it over the net.
p.10
Vertical and Horizontal Motion of Projectiles
What is the relationship between two projectiles with the same initial vertical velocity?
They will reach the same height at the same time, regardless of mass and horizontal velocity.
p.2
Newton's Laws of Motion
What misconception exists about the net force on an inclined plane?
The net force does not always point in the direction of motion.
p.15
Projectile Motion Basics
What are the horizontal and vertical components of the ball’s initial velocity vector when thrown at 30° with an initial velocity of 10 m/s?
Horizontal: 10 × cos(30°), Vertical: 10 × sin(30°)
p.9
Vertical and Horizontal Motion of Projectiles
How can the vertical motion of projectiles be analyzed?
By resolving the velocity vector into its vertical and horizontal components.
p.16
Effects of Air Resistance on Projectiles
What is air resistance?
A force applied by the air on a projectile, opposing its motion through the air.
p.1
Friction on Inclined Planes
What is friction?
A force that resists the relative motion of two surfaces in contact.
p.11
Vertical and Horizontal Motion of Projectiles
What happens to the vertical velocity of a projectile launched horizontally over time?
It starts from zero and increases with time.
p.11
Newton's Laws of Motion
What equations are used to model the vertical motion of projectiles?
Equations of constant acceleration.
p.1
Forces on Inclined Planes
What direction does the normal force act on an inclined plane?
Perpendicular to the plane.
p.8
Friction on Inclined Planes
What is the magnitude of the ball’s acceleration as the friction force slows it down?
To be calculated based on the friction force.
p.2
Components of Gravitational Force
What symbols are used to represent parallel and perpendicular forces on inclined planes?
The symbol '∥' represents parallel and '⊥' represents perpendicular.
How is the net force acting on an object sliding down an inclined plane calculated?
F_net∥ = m * g * sin(θ) - F_f.
What is the formula for the net force on an object sliding up an inclined plane?
F_net∥ = m * g * sin(θ) + F_f.
p.19
Projectile Motion Basics
What is the formula to calculate the range of a projectile?
Range = (initial velocity^2 * sin(2 * angle)) / g, where g is the acceleration due to gravity.
p.10
Vertical and Horizontal Motion of Projectiles
How is vertical displacement represented in projectile motion?
As the change in height of the object.
p.16
Effects of Air Resistance on Projectiles
In which directions does air resistance act on a projectile?
In both the vertical and horizontal directions.
p.18
Vertical and Horizontal Motion of Projectiles
How far from the base of the cliff does the arrow land if it has a horizontal velocity of 60 m/s?
Distance = horizontal velocity × time. Thus, distance = 60 m/s × 2.86 s ≈ 171.6 m.
p.2
Friction on Inclined Planes
How does friction affect an object on an inclined plane?
Friction acts parallel to the plane and opposes the direction of motion.
p.12
Vertical and Horizontal Motion of Projectiles
What is the relationship between horizontal and vertical motion of a projectile?
The horizontal motion is independent of its vertical motion.
What is the formula for the net perpendicular force on an object on an inclined plane?
F_net⊥ = F_N - m * g * cos(θ).
p.9
Newton's Laws of Motion
What equations can be used to solve problems involving vertical motion of projectiles?
Equations of constant acceleration.
p.1
Inclined Plane Definition
What is an inclined plane?
A flat surface that is at an angle to the horizontal plane.
What is the equation for the net force acting perpendicular to an inclined plane?
F_net⊥ = F_N - m g cos(θ)
p.14
Projectile Motion Basics
What theorem is used to determine the magnitude of the velocity from its components?
Pythagoras' theorem: v² = v_x² + v_y².
p.9
Projectile Motion Basics
What does 'range' refer to in projectile motion?
The horizontal distance a projectile travels.
p.9
Projectile Motion Basics
What factors affect a projectile's motion, flight time, and maximum range?
Initial velocity, launch angle, and air resistance.
p.11
Vertical and Horizontal Motion of Projectiles
What does the symmetry of vertical motion imply about the vertical velocity of a projectile?
The magnitude of the vertical velocity is the same going up or down; only the direction changes.
p.19
Projectile Motion Basics
What is the maximum height above the cliff that the stone reaches when launched at 40° with a speed of 75 m/s?
Maximum height can be calculated using the vertical component of the initial velocity.
p.6
Forces on Inclined Planes
Why does the normal force not affect the motion of the block on the inclined plane?
Because the normal force acts perpendicular to the motion and does not contribute to the net force parallel to the incline.
p.4
Forces on Inclined Planes
What forces does an object on an inclined plane experience?
Gravity and a normal force, and sometimes friction.
What happens to the acceleration of an object on an inclined plane as the angle of inclination increases?
The magnitude of this acceleration increases.
p.4
Forces on Inclined Planes
Why do objects on an inclined plane have no net force perpendicular to the plane?
The normal force and the perpendicular component of the gravitational force are equal and opposite.
p.9
Projectile Motion Basics
How can skilled gunners maximize the range of cannonballs?
By firing near the top of the ship’s roll.
p.20
Projectile Motion Basics
What is the theoretical range of a projectile launched at an initial speed of 15 m/s and at an angle of 40°?
To calculate: R = (15² * sin(80°)) / g (where g = 9.81 m/s²).
p.20
Effects of Air Resistance on Projectiles
If the students measure a maximum range of 22.2 m, can the effect of air resistance be ignored?
No, because the measured range may differ significantly from the theoretical range without air resistance.
p.1
Components of Gravitational Force
What component of gravitational force acts down the inclined plane?
The component of gravitational force parallel to the plane.
p.15
Vertical and Horizontal Motion of Projectiles
What is the formula used to calculate the vertical position of the ball after 2.46 seconds?
s = u_y * t + 1/2 * a * t^2
p.19
Vertical and Horizontal Motion of Projectiles
How can you calculate the height of the table from which Mark rolls the ball?
Height = 0.5 * g * t^2, where g is the acceleration due to gravity and t is the time of flight.
p.8
Forces on Inclined Planes
What data does Finn collect while Garrett skateboards?
The angle of inclination and the net force on Garrett.
p.6
Forces on Inclined Planes
Why do we subtract the friction force from the parallel component of gravitational force on an inclined plane?
To find the net force acting on the block, as friction opposes the motion.
p.14
Projectile Motion Basics
How can the velocity vector of a projectile be resolved?
Into a horizontal component (v_x = v cos(θ)) and a vertical component (v_y = v sin(θ)).
p.9
Effects of Air Resistance on Projectiles
What is air resistance?
The force of air particles resisting the motion of objects through the air.
p.1
Forces on Inclined Planes
Why do ski racers try to stay in constant contact with the slope?
To move as fast as possible parallel to the hill and maintain acceleration towards the finish line.
p.11
Net Force Calculation
How long does it take for a ball launched upwards at 19 m/s to reach maximum height?
Approximately 1.9 seconds.
p.13
Projectile Motion Basics
What impact does the launch angle have on a projectile?
It affects how far and high the projectile travels.
p.6
Friction on Inclined Planes
What is the frictional force acting on a 1.2 kg block of wood sliding down an inclined plane?
F_f = 1.7 N (up the plane).
p.17
Projectile Motion Basics
What is the magnitude of the initial vertical velocity of the ball?
The initial vertical velocity can be calculated using the formula: u_y = u * sin(θ), where u = 10 m/s and θ = 40°. Therefore, u_y = 10 * sin(40°) ≈ 6.43 m/s.
p.17
Projectile Motion Basics
Calculate the time it takes the ball to travel to the net.
Time can be calculated using the formula: t = distance / horizontal velocity. The distance to the net is 8.0 m and the horizontal velocity is approximately 7.66 m/s. Therefore, t = 8.0 / 7.66 ≈ 1.04 seconds.
p.18
Projectile Motion Basics
What height above the ground does the soccer ball hit the wall if kicked at an angle of 20° with an initial speed of 25 m/s and the wall is 29 m away?
Using the horizontal motion to find time and then vertical motion to find height, the height can be calculated as approximately 2.5 m.
p.5
Components of Gravitational Force
How can the gravitational force on an inclined plane be resolved?
Into two components: parallel (F_g∥) and perpendicular (F_g⊥) to the plane.
p.12
Horizontal Motion of Projectiles
What happens to the horizontal velocity of a projectile when air resistance is ignored?
It remains constant throughout the projectile’s motion.
p.20
Newton's Laws of Motion
What is the force exerted on Marie by the couch?
The force is equal to Marie's weight, which is 70 kg * g (where g = 9.81 m/s²).
p.20
Forces on Inclined Planes
How do you calculate the angle of banking for a cyclist on a banked track?
Using the formula: tan(θ) = v² / (r * g).
p.19
Projectile Motion Basics
How do you calculate the horizontal distance to point A from the cliff?
Horizontal distance = horizontal velocity * total time of flight.
p.17
Projectile Motion Basics
What is the magnitude of the initial horizontal velocity of the ball?
The initial horizontal velocity can be calculated using the formula: u_x = u * cos(θ), where u = 10 m/s and θ = 40°. Therefore, u_x = 10 * cos(40°) ≈ 7.66 m/s.
p.11
Projectile Motion Basics
Can we apply the symmetry of vertical motion to a horizontally launched projectile?
No, because the projectile begins at its maximum height.
p.16
Projectile Motion Basics
What characterizes the vertical motion of a projectile?
There is a constant acceleration downwards due to gravity.
p.2
Forces on Inclined Planes
What is the relationship between the normal force and the gravitational force on an inclined plane?
The normal force is equal in magnitude and opposite in direction to the perpendicular component of gravitational force.
p.15
Projectile Motion Basics
Does the player score if the ball must pass over a bar that is 3.0 m high?
Yes, the player scores as 6.26 m > 3.0 m.
p.10
Vertical and Horizontal Motion of Projectiles
What does the vertical component of the initial velocity represent?
uₓ (initial vertical velocity).
p.2
Forces on Inclined Planes
What two forces always act on an object on an inclined plane?
The force due to gravity and the normal force.
p.5
Forces on Inclined Planes
What are the three main forces acting on an object on an inclined plane?
Gravitational force, normal force, and friction force.
p.12
Projectile Motion Basics
What must be correct when a person throws a ball vertically upwards and it lands on a shelf lower than the height it was thrown from?
The ball’s velocity is zero at the top of the flight.
p.14
Projectile Motion Basics
What is the first step in analyzing projectile motion?
Determine whether the horizontal or vertical direction determines the end of the projectile motion.
p.14
Projectile Motion Basics
What is the initial velocity of the rugby ball kicked towards the goal?
19 m/s at an angle of 50° from the horizontal.
p.19
Vertical and Horizontal Motion of Projectiles
What is the magnitude of the velocity of the ball when it hits the floor?
The magnitude can be calculated using the horizontal and vertical components of velocity at impact.
p.7
Inclined Plane Definition
How does the magnitude of Garrett’s acceleration compare at points P, Q, and R?
It varies depending on the slope of the inclined planes at each point.
p.17
Vertical and Horizontal Motion of Projectiles
Which formula can be used to find the height of the ball when it reaches the net?
B. s_y = u_y t + 1/2 a t² can be used to find the height of the ball when it reaches the net.
What is the formula for the net force acting on an object moving up an inclined plane?
F_net = m g sin(θ) + F_f.
What happens to the net force down the plane if the angle of inclination is increased?
The net force down the plane and the acceleration down the plane will increase.
p.19
Vertical and Horizontal Motion of Projectiles
What is the speed of Isaac’s stone as it hits the water?
The speed can be calculated using the conservation of energy or kinematic equations.
p.12
Horizontal Motion of Projectiles
What can be said about the instantaneous velocity of a projectile in the horizontal direction?
It is the same as its average velocity.
p.19
Projectile Motion Basics
Will Isaac’s stone sink the enemy's boat if it hits with a speed greater than 70.0 m/s?
Yes, if the speed of the stone upon impact exceeds 70.0 m/s, the boat will sink.
