Projectile Motion Concepts

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Questions and Answers

What is the initial vertical velocity of the ball?

  • -5 m/s
  • 0 m/s (correct)
  • -10 m/s
  • 20 m/s

What is the acceleration in the y direction as the ball falls?

  • 9.8 m/s²
  • 20 m/s²
  • -9.8 m/s² (correct)
  • 0 m/s²

How long does it take for the ball to fall to the ground?

  • 0.5 seconds
  • 2 seconds
  • 1 second (correct)
  • 0 seconds

What is the final vertical velocity of the ball just before it strikes the ground?

<p>-10 m/s (A)</p> Signup and view all the answers

Using the Pythagorean theorem, what is the resultant velocity of the ball just before it strikes the ground?

<p>22.36 m/s (B)</p> Signup and view all the answers

Which formula is used to find the final velocity in the y direction?

<p>vfy = viy + at (B)</p> Signup and view all the answers

What is the horizontal velocity of the ball?

<p>20 m/s (B)</p> Signup and view all the answers

What is the horizontal acceleration of the ball?

<p>0 m/s² (C)</p> Signup and view all the answers

What distinguishes a scalar quantity from a vector quantity?

<p>A scalar quantity is just a number, while a vector quantity is a number with a direction. (D)</p> Signup and view all the answers

In projectile motion, which component of velocity remains constant?

<p>The horizontal component remains constant while the vertical component changes. (A)</p> Signup and view all the answers

Which statement about the ideal path of a projectile is true?

<p>Time of ascent equals time of descent. (A)</p> Signup and view all the answers

What mathematical principle is used to calculate the magnitude of the resultant vector from its components?

<p>Pythagorean Theorem. (B)</p> Signup and view all the answers

In vector addition, which step should be taken first to find the resultant vector?

<p>Sum up all vectors in the y-direction. (C)</p> Signup and view all the answers

What does a vector represent in the context of projectile motion?

<p>A quantity with both magnitude and direction. (C)</p> Signup and view all the answers

Which component is affected by gravity during projectile motion?

<p>Only the vertical component is affected. (A)</p> Signup and view all the answers

What is the acceleration due to gravity during free fall?

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

What shape does the path of a projectile typically follow in ideal conditions?

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

In projectile motion, how does velocity change in the x direction?

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

Using the equation for vertical motion, y = ½ at², what does 'a' represent?

<p>The acceleration due to gravity. (C)</p> Signup and view all the answers

What is the initial vertical velocity (viy) of an object that is dropped?

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

What does the term 'dy' represent in vertical motion equations?

<p>The change in vertical position. (A)</p> Signup and view all the answers

If a projectile is launched at a horizontal distance of 20m and falls 5m vertically, how long is the ball in the air?

<p>1 second (B)</p> Signup and view all the answers

Which equation can be used to determine the horizontal position of a projectile?

<p>x = vt (B)</p> Signup and view all the answers

When a projectile is launched, how does its path compare to the ideal straight-line path without gravity?

<p>It falls below the straight-line path due to gravity. (B)</p> Signup and view all the answers

Flashcards

Scalar Quantity

A quantity that has only magnitude (size). It's just a number, like your weight on a scale.

Vector Quantity

A quantity that has both magnitude (size) and direction. Imagine an arrow pointing in a specific direction.

Resolving a Vector

Breaking a vector (like velocity) into two components that are perpendicular to each other, typically horizontal and vertical.

Trajectory of a Projectile

The path that a projectile follows through the air, shaped like a curve.

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Horizontal Velocity Component

The component of the velocity that doesn't change as the projectile moves. It stays constant.

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Vertical Velocity Component

The component of the velocity that changes due to gravity's pull. It gets slower going up and faster coming down.

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Ideal Projectile Motion

A projectile's motion where we ignore air resistance, making its path a symmetrical parabola.

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Pythagorean Theorem

A mathematical theorem that relates the sides of a right triangle: The square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

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What is 'a' in free fall?

The constant acceleration due to gravity, pulling all objects downwards towards the Earth. Its value is approximately -9.81 m/s².

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What is the trajectory of a projectile?

The path a projectile takes through the air, shaped like a curve due to the combination of horizontal motion and vertical acceleration from gravity.

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What is the horizontal velocity of a projectile?

The horizontal component of a projectile's velocity remains constant throughout its flight because there is no horizontal force acting on it.

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What is the vertical velocity of a projectile?

The vertical component of a projectile's velocity changes due to gravity's constant downward acceleration. It slows down as the projectile goes up and speeds up as it comes down.

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What is the time of flight of a projectile?

The time it takes for a projectile to complete its entire flight, from launch to landing. It depends on factors like initial vertical velocity and height.

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What is the range of a projectile?

The distance a projectile travels horizontally from its launch point to its landing point. It depends on horizontal velocity and time of flight.

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What is the initial velocity of a projectile?

The initial velocity of a projectile, which can be broken down into horizontal and vertical components. It determines the projectile's initial direction and speed.

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What is the maximum height of a projectile?

The maximum height that a projectile reaches during its flight. It depends on the projectile's initial vertical velocity and the strength of gravity.

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Instantaneous Velocity

The velocity of an object at a specific moment in time, considering both its speed and direction.

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Acceleration

The rate of change of velocity over time. A positive acceleration means the object is speeding up, while a negative acceleration means it's slowing down.

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Vector

A quantity that has both magnitude (size) and direction.

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Horizontal Velocity of a Projectile

The horizontal component of the velocity of a projectile remains constant throughout its motion if air resistance is negligible. This means the projectile travels at a steady speed in the horizontal direction.

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Vertical Velocity of a Projectile

The vertical component of the velocity of a projectile changes due to the influence of gravity. It slows down as it goes up and speeds up as it comes down.

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Resultant Velocity of a Projectile

The overall velocity of a projectile at the moment it impacts the ground. It's calculated by combining the horizontal and vertical velocity components.

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Study Notes

Projectile Motion

  • Projectile motion is the motion of an object thrown or projected into the air, subject to only the force of gravity.
  • Scalars are just numbers, like weight.
  • Vectors have both magnitude and direction, like velocity.
  • A vector can be resolved into two components.
  • Component vectors form right angles to each other.
  • An example of a component is the vertical component of the velocity and horizontal component of the velocity.
  • Projectile motion follows a parabolic path.
  • The horizontal component of velocity stays constant.
  • The vertical component of velocity changes due to gravity's effect.
  • Ideal projectile paths (no air resistance) have equal time up and down, and equal velocities up and down.
  • The actual path of a projectile may be different due to the presence of air resistance.
  • To add vectors mathematically:
    • Sum the x-direction vectors (Σx).
    • Sum the y-direction vectors (Σy).
    • Draw Σx and Σy vectors head-to-tail, including direction.
    • Draw the resultant vector (from start to end).
    • Use the Pythagorean theorem to find the resultant vector's size.
  • The Pythagorean theorem states: C² = A² + B². (C is the hypotenuse, A and B are legs).
  • Examples of projectiles include cannonballs, stones, and spacecraft in orbit.
  • All objects experience a downward acceleration due to gravity (g = -9.81 m/s²).
  • Horizontal motion is unaffected by gravity (constant horizontal velocity).
  • Vertical motion is affected by gravity. The formula for vertical displacement (y) is: y = 0.5 * a * t².
  • In the x-direction, gravity has no effect. The velocity is constant. Horizontal position can be found by x = vt.
  • In the y-direction, gravity pulls downward. The y-position is given by y = 0.5 * a * t².
  • The actual projectile path is the combination of the vertical and horizontal motions.
  • Projectile motion examples: monkey, ballistics, juggling, moon feather.
  • To find the time in the air, use the vertical displacement equation. Use the constant velocity equation to solve for velocity in another direction.
  • To find resultant velocity, use Pythagorean theorem and the equation for both x and y directions.

Equations

  • Horizontal (x):

    • Vfx = dx/t
    • dx = Vix * t + 0.5 * ax * t²
    • Vfx² = Vix² + 2 * ax * dx

  • Vertical (y):

    • Vfy = Viy + ay * t
    • dy = Viy * t + 0.5 * ay * t²
    • Vfy² = Viy² + 2 * ay * dy

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