Physics Projectile Motion Quiz

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Questions and Answers

If an object is moving in the positive direction and its velocity is decreasing, what is the sign of its linear acceleration?

  • - (correct)
  • It is impossible to determine without more information.
  • 0
  • +

A ball is thrown vertically upwards. What is the sign of the ball's vertical acceleration as it rises?

  • +
  • 0
  • - (correct)
  • It is impossible to determine without more information.

A projectile is launched horizontally with an initial velocity of 20 m/s. What is the projectile's horizontal velocity 2 seconds later, assuming negligible air resistance?

  • 0 m/s
  • 40 m/s
  • 10 m/s
  • 20 m/s (correct)

A shotput is launched at an angle of 40° above the horizontal with an initial velocity of 13.3 m/s. What is the initial vertical velocity of the shotput?

<p>8.55 m/s (B)</p> Signup and view all the answers

A ball is thrown vertically upwards. What is its vertical velocity at the highest point of its trajectory?

<p>0 m/s (C)</p> Signup and view all the answers

A projectile is launched horizontally with an initial velocity of 10 m/s. What is the projectile's vertical acceleration?

<p>-9.81 m/s² (C)</p> Signup and view all the answers

A shotput is launched at an angle of 40° above the horizontal. What is the shotput's horizontal velocity at the highest point of its trajectory?

<p>10.2 m/s (C)</p> Signup and view all the answers

What is the initial vertical velocity ($v_i$) of the projectile?

<p>8.55 m/s (B)</p> Signup and view all the answers

Which of the following equations represents the final velocity ($v_f$) of the projectile in terms of the initial velocity ($v_i$), acceleration ($a$), and time ($t$)?

<p>$v_f = v_i + at$ (A)</p> Signup and view all the answers

What is the final vertical position ($s_f$) of the projectile?

<p>5.92 m (D)</p> Signup and view all the answers

What are the units for acceleration ($a$)?

<p>m/s$^2$ (A)</p> Signup and view all the answers

What factors influence a projectile's trajectory?

<p>Gravity and projection parameters (D)</p> Signup and view all the answers

If two projectiles are launched from the same height with different angles but the same initial velocity, what will be true about their horizontal velocities at the apex of flight?

<p>Both will be equal to the initial horizontal velocity (D)</p> Signup and view all the answers

How does the projection velocity affect a projectile's motion?

<p>It influences both maximum height and range (A)</p> Signup and view all the answers

What happens to the vertical velocity of a projectile immediately before ground contact, assuming equal projection and landing heights?

<p>It is equal and opposite to the vertical velocity at launch (D)</p> Signup and view all the answers

What is the relative projection height when the takeoff height is equal to the landing height?

<p>Equal to zero (C)</p> Signup and view all the answers

Which of the following best describes the vertical velocity of a projectile at its apex?

<p>It is zero (B)</p> Signup and view all the answers

If a projectile is launched with a high angle, what is likely to be true about its horizontal and vertical velocities?

<p>Vertical velocity will dominate over horizontal velocity (D)</p> Signup and view all the answers

What effect does air resistance have on a projectile's motion?

<p>It reduces the maximum height (B)</p> Signup and view all the answers

What is the final velocity (Vf) of the object if the initial velocity (Vi) is 0 m/s and the acceleration (a) is -9.81 m/s² for a time interval of 1.96 s?

<p>-10.78 m/s (D)</p> Signup and view all the answers

Which formula correctly represents the motion of an object given its final velocity, initial velocity, acceleration, and displacement?

<p>$v_f^2 = v_i^2 + 2a(s_f - s_i)$ (A), $v_f = v_i + a(t_f - t_i)$ (B)</p> Signup and view all the answers

In a projectile motion scenario, if the range (R) formula includes the term $v_r^2 imes ext{sin}( heta) imes ext{cos}( heta)$, what does $v_r$ represent?

<p>Resultant velocity (A)</p> Signup and view all the answers

What is the value of displacement (Si) when the initial height is stated as 5.92 m?

<p>5.92 m (B)</p> Signup and view all the answers

If an object is falling vertically with an initial velocity of 0 m/s, and the acceleration due to gravity is -9.81 m/s², what can be inferred about its motion over time?

<p>Its velocity will increase in the positive direction. (C)</p> Signup and view all the answers

If the vertical displacement is defined as 0 when the object reaches the ground (Sf = 0 m), what does this indicate about the starting height?

<p>The object started from a height of 5.92 m. (B)</p> Signup and view all the answers

Which of the following is true about an object's time of flight in projectile motion based on the provided values?

<p>It varies with the angle of projection. (B), It is calculated as $t_f = 2 h / g$. (C)</p> Signup and view all the answers

Which condition would lead to the maximum range of a projectile when using the range formula?

<p>A launch angle of 45 degrees. (A)</p> Signup and view all the answers

What is the formula to determine final velocity given initial velocity, acceleration, and time?

<p>𝑣𝑓 = 𝑣𝑖 + 𝑎∆𝑡 (D)</p> Signup and view all the answers

In projectile motion, which component is influenced by acceleration due to gravity?

<p>Vertical component (D)</p> Signup and view all the answers

Which equation can be used to determine the displacement of an object under constant acceleration?

<p>𝑠𝑓 = 𝑠𝑖 + 𝑣𝑖 ∆𝑡 + 𝑎∆𝑡^2 (D)</p> Signup and view all the answers

For a field goal kicker who kicks the ball at 30 m/s at a 30° angle, which component represents the vertical launch velocity?

<p>30 sin(30°) (B)</p> Signup and view all the answers

How is acceleration estimated graphically?

<p>By determining the slopes of the velocity-time graph (A)</p> Signup and view all the answers

What does the range formula for projectile motion include in terms of initial velocities and angles?

<p>$R = \frac{v_r^2 \cdot sin(2\theta)}{g}$ (C)</p> Signup and view all the answers

Which formula accurately expresses the relationship between velocity, distance, and time?

<p>$v = \frac{\Delta s}{\Delta t}$ (B)</p> Signup and view all the answers

What is the effect of horizontal motion on projectile acceleration when neglecting air resistance?

<p>It remains constant (D)</p> Signup and view all the answers

When calculating the slope using rise over run, which quantities are used?

<p>Change in position over change in time (A)</p> Signup and view all the answers

What is the trajectory of a projectile in the absence of air resistance?

<p>A parabola (B)</p> Signup and view all the answers

What is the vertical acceleration of a projectile?

<p>-9.81 m/s^2 (A)</p> Signup and view all the answers

At the apex of its trajectory, what is the vertical velocity of a projectile?

<p>Zero (D)</p> Signup and view all the answers

What is the horizontal acceleration of a projectile?

<p>0 m/s^2 (A)</p> Signup and view all the answers

Why is it important to analyze the horizontal and vertical components of projectile motion separately?

<p>Because they are independent of each other. (D)</p> Signup and view all the answers

What is the distance travelled in the vertical component of a projectile's motion?

<p>The distance from the starting position to the highest point of the trajectory (A)</p> Signup and view all the answers

Why is air resistance considered negligible in projectile motion?

<p>Because it is always very small. (C)</p> Signup and view all the answers

What is the primary force acting on a projectile in motion?

<p>Gravity (A)</p> Signup and view all the answers

Flashcards

Projectile

An object projected into the air, moving under gravity and air resistance.

Flight path

The trajectory of a projectile, typically a parabola in absence of air resistance.

Vertical component

The part of projectile motion influenced by gravity, affecting height.

Gravity's acceleration

Constant vertical acceleration of -9.81 m/s² acting on projectiles.

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Horizontal component

The part of projectile motion that moves in a straight line without external forces.

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Velocity at apex

At the top of the trajectory, the vertical velocity of a projectile is 0 m/s.

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Air resistance

Opposing force acting on projectiles, considered negligible in basic projectile motion.

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Constant horizontal velocity

Horizontal motion of a projectile with zero acceleration; the speed does not change.

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Initial Velocity (Vi)

The speed of an object at the start of its motion, measured at 8.55 m/s upward.

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Final Velocity (Vf)

The speed of an object when it reaches the apex of its motion, which is 0 m/s at the highest point.

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Time of Flight (tf)

The total time the object is in the air before hitting the ground, calculated as 0.87 seconds.

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Vertical Displacement (sf)

The height reached by the projectile, ending at 5.92 meters after starting from 2.2 meters.

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Acceleration due to Gravity (a)

The constant downward acceleration experienced by the projectile, equal to -9.81 m/s².

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Linear Acceleration

The rate of change of velocity of an object in motion.

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Positive Direction Acceleration

Increasing velocity in a positive direction means acceleration is positive.

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Negative Direction Acceleration

Decreasing velocity in a positive direction or increasing velocity in a negative direction.

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Horizontal Velocity (vx)

The constant velocity of an object moving horizontally in projectile motion.

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Vertical Velocity (vy)

The changing velocity of an object in the vertical direction, typically under gravity.

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Acceleration due to Gravity

In vertical motion, the constant rate of -9.81 m/s² that objects accelerate downwards.

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Projectile Motion

The motion of an object thrown into the air, subject to gravity and with constant horizontal velocity.

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Shotput Example Breakdown

To solve projectile problems, split motion analysis into vertical and horizontal components.

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Displacement (Si)

The initial position of an object; Si = 5.92 m for vertical descent.

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Range of a projectile (R)

The horizontal distance a projectile travels; calculated with a formula involving angles.

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Vertical range formula

R = (vy * vr * sin(θ) * cos(θ) + vx * vy² + 2gh) / g.

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Projectile motion components

Motion can be resolved into horizontal (vx) and vertical (vy) aspects affecting the flight.

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Projectile Motion Influencers

Factors affecting a projectile’s trajectory, including gravity and projection parameters.

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Apex of Flight

The highest point reached by a projectile where vertical velocity is 0 m/s.

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Relative Projection Height (RPH)

Difference between takeoff and landing vertical positions; helps categorize projectile paths.

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Projection Velocity

The speed at which a projectile is launched; influences range and height of flight.

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Projection Angle

The angle at which a projectile is launched; affects horizontal and vertical velocity components.

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Vertical Velocity Midway

The vertical component of velocity at the midpoint in a projectile’s flight is influenced by gravity.

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Horizontal Velocity

Constant velocity of a projectile in horizontal motion when air resistance is negligible.

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Constant Acceleration Equations

Mathematical formulas used to analyze projectile motion, accounting for gravity and time.

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Final Velocity Formula

The formula to calculate final velocity: vf = vi + a∆t.

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Displacement Equation

Displacement relates initial position, final position, and speed over time: sf = si + vi∆t + (1/2)a∆t².

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Vertical Component Acceleration

The vertical motion of projectiles is influenced by gravity, with an acceleration of -9.81 m/s².

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Horizontal Component of Motion

The horizontal component of projectiles moves with zero acceleration, remaining constant.

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Range of Projectile

The formula to determine how far a projectile travels: R = (v^2 * sin(2θ)) / g.

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First Central Difference Method

A method to estimate velocity using surrounding data points: vi = (x(i+1) - x(i-1)) / (t(i+1) - t(i-1)).

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Acceleration Formula

The change in velocity over time, calculated as a = (vf - vi) / ∆t.

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Motion Analysis for Projectiles

Breaking down projectile motion into separate vertical and horizontal motions helps simplify calculations.

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Vertical Displacement

The height of a projectile from its starting point to its peak height.

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Slope in Motion Analysis

The slope of position-time graphs indicates speed, calculated as rise/run.

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Study Notes

Projectile Motion

  • Bodies projected into the air are projectiles
  • The only forces acting on a projectile are gravity and air resistance
  • In the absence of air resistance, a projectile's flight path is a parabola
  • Projectiles have both vertical and horizontal components
  • These components must be analyzed separately
  • The vertical component is affected by gravity, resulting in a constant vertical acceleration of -9.81 m/s²
  • The horizontal component is not affected by any external forces, so the horizontal acceleration is 0 m/s²
  • Horizontal velocity remains constant
  • Vertical velocity changes due to gravity
  • At the apex (highest point), vertical velocity is 0 m/s

Projectile Motion Equations

  • vf = vi + a∆t
  • Sf = Si + vi∆t + ½ a∆t²
  • vf² = vi² + 2a(Sf - Si)
  • Range (R) = (vi² sin2θ)/g + vx * √(2*h/g)

Solving Projectile Motion Problems

  • Break the problem into manageable components (vertical up, vertical down, horizontal)
  • Use appropriate equations for each component
  • Examples of problem solving methods are shown in the slides

Additional Concepts

  • Interpreting Linear Acceleration: This section explains the relationship between acceleration and velocity changes when moving in the positive and negative directions.
  • The influence of projection angle affects the relative magnitude of horizontal and vertical velocities for projectiles to calculate maximum range and height.
  • Relative Projection Height: (RPH) = Vertical take-off position - Vertical landing position. RPH = 0 if take off and landing positions are the same. RPH > 0 if take off is higher than landing. RPH < 0 if take off is lower than landing.
  • Air resistance is usually ignored for projectile motion problems in introductory physics.

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