ch 3 physics

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Questions and Answers

What is the correct formula to calculate the horizontal displacement of a projectile?

  • x = v_y * t
  • x = v_x * t (correct)
  • x = v_i * t
  • x = v * sin(θ) * t

If a projectile is launched horizontally off a 22.0-meter high hill, how can its time of flight be determined?

  • Using the equation t = h/g
  • By using the horizontal velocity and calculating distance
  • Using the equation t = √(2h/g) (correct)
  • By directly measuring the horizontal distance covered

In projectile motion, what does the component v_x represent?

  • The total velocity of the projectile
  • The vertical velocity component
  • The horizontal velocity component (correct)
  • The time of flight of the projectile

When considering projectile motion, how is the vertical component of velocity (v_y) calculated?

<p>v_y = v * sin(θ) (C)</p> Signup and view all the answers

If a projectile is launched at an angle of 30 degrees with an initial velocity of 10 m/s, what can be said about its horizontal motion?

<p>The horizontal velocity component is determined by v_x = v * cos(30°) (D)</p> Signup and view all the answers

What must be done before adding two or more vectors together?

<p>Convert them to Cartesian coordinates (A)</p> Signup and view all the answers

Which formula represents the x-component of a vector A?

<p>$A_x = A ext{cos} heta$ (D)</p> Signup and view all the answers

Which analytical method is more concise and accurate for vector operations?

<p>Analytical methods using trigonometry (D)</p> Signup and view all the answers

In projectile motion, what is the behavior of the x and y components of the motion?

<p>They are independent and analyzed separately (D)</p> Signup and view all the answers

What is used to find the magnitude of the resultant vector from its components?

<p>The Pythagorean theorem (B)</p> Signup and view all the answers

If an object is projected horizontally, which of the following statements is true about its motion?

<p>The horizontal component of velocity remains constant (D)</p> Signup and view all the answers

What is the effect of gravitational force on the motion of a projectile?

<p>It only affects the vertical motion (D)</p> Signup and view all the answers

Which equation would you use to find the direction of a vector R when given its components?

<p>$ heta = ext{tan}^{-1} rac{A_y}{A_x}$ (A)</p> Signup and view all the answers

What is the graphical method called that is used for vector addition?

<p>Head-to-Tail Method (C)</p> Signup and view all the answers

If a vector A has a magnitude of 10 km north and vector B has a magnitude of 5 km west, what is the resultant vector A + B?

<p>12.5 km at 63.43 degrees (C)</p> Signup and view all the answers

When subtracting vector B from vector A graphically, what does 'A - B' represent?

<p>Vector A added to the negative of vector B (B)</p> Signup and view all the answers

If vector A has a magnitude of 6 and points north, and vector B has a magnitude of 8 and points east, what is the magnitude of B - A?

<p>10 km (C)</p> Signup and view all the answers

What happens to the magnitude and direction of a vector when it is multiplied by a negative scalar?

<p>Magnitude remains the same, direction reverses (A)</p> Signup and view all the answers

What is required to determine the direction of the resultant vector in vector addition?

<p>The angle it makes with the reference frame (B)</p> Signup and view all the answers

How is the negative of vector B represented graphically?

<p>It is the same length but points in the opposite direction (C)</p> Signup and view all the answers

What does vector addition being commutative imply?

<p>The order of adding vectors does not affect the resultant (B)</p> Signup and view all the answers

Flashcards

Vector Components

Representing a vector using its 'x' and 'y' components (e.g. (x,y)).

Vector Addition

Adding vectors by adding their corresponding x- and y-components first and then use the Pythagorean theorem and arctangent formulas.

Analytical methods in vector addition

Utilizing geometry and trigonometry to determine the vector accurately.

Projectile Motion

The motion of an object thrown or projected under the influence of gravity.

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Independent Axes in Projectile Motion

Horizontal and vertical motions of a projectile are independent and unaffected by each other.

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Horizontal Projectile

A projectile launched horizontally, only affected by gravity.

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Horizontal Displacement of Projectile

Dependent on the initial horizontal velocity.

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Projectile Motion Analysis Steps

Resolve motion into horizontal and vertical components; treat horizontal and vertical motions independently; solve for unknowns in each direction, often using time as a link between them; recombine the motions to determine results.

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Projectile horizontal displacement

The horizontal distance traveled by a projectile, calculated by multiplying the initial horizontal velocity (vix) by the time of flight (t).

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Horizontal velocity (vix)

The initial velocity of a projectile in the horizontal direction. It remains constant throughout the projectile's flight.

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Time of flight (t)

The total time a projectile takes to travel from its launch point to the ground

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Horizontal displacement calculation

Calculating the horizontal distance traveled by a projectile can be done by multiplying the horizontal components of initial velocity and the time in air

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Components of projectile velocity

The horizontal (vx) and vertical (vy) velocity components of a projectile, calculated using trigonometric functions.

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Two-dimensional kinematics

Describing motion along a curved path on a flat surface.

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Vector quantity

A quantity described by both magnitude and direction.

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Scalar quantity

A quantity described only by its magnitude.

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Vector addition (head-to-tail)

A graphical method to add two or more vectors by connecting the tail of one vector to the head of another.

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Vector subtraction

Adding the negative of the vector to be subtracted to the other vector.

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Resultant vector

The vector sum of two or more vectors.

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Vector multiplication by a scalar

The vector's magnitude changes by the value of the scalar; direction changes if the scalar is negative.

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Commutative property of vector addition

The order of vectors doesn't affect the result of the addition.

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Study Notes

Two Dimensional Kinematics

  • Two-dimensional kinematics describes motion along a curved path on a flat surface, like a ball on a pool table or a skater on an ice rink.
  • A vector quantity is fully described by magnitude and direction (e.g., velocity).
  • A scalar quantity is fully described by magnitude alone (e.g., speed).

Vector Addition and Subtraction - Graphical Method

  • The head-to-tail method: The tail of the second vector is placed at the head of the first vector. The resultant vector starts at the tail of the first vector and ends at the head of the second vector.
  • Vector addition is commutative: A + B = B + A.

Vector Addition and Subtraction - Analytical Method

  • Analytical methods use geometry and trigonometry to find the resultant vector.
  • Cartesian components: These are the projections of a vector onto the x and y axes.
  • To find the components, use trigonometry: Ax = A cos θ and Ay = A sin θ.
  • Once the components are found, add the x-components and the y-components separately to obtain the resultant vector.

Projectile Motion

  • Projectile motion is the motion of an object thrown or projected into the air, affected only by gravity.
  • The path of a projectile is called the trajectory.
  • Horizontal and vertical motions are independent.
  • The horizontal motion has constant velocity (ax = 0).
  • The vertical motion has constant acceleration (ay = -g).

Projectile Motion Analysis Steps

  • Resolve the motion into horizontal (x) and vertical (y) components.
  • Treat horizontal and vertical motions separately.
  • Solve for the unknowns (typically time) using appropriate kinematic equations in each direction.
  • Combine the horizontal and vertical components to find the overall displacement and velocity.

Horizontally Launched Projectiles

  • The horizontal displacement of a horizontally launched projectile is given by x = vix * t.

Examples of Projectile Problems

  • Various projectile motion examples are given (varying launch heights, angles, and initial velocities).

Determining Components of a Velocity Vector

  • The horizontal component of velocity is vx = v cos θ
  • The vertical component of velocity is vy = v sin θ

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Chapter 3: Two Dimensional Kinematics PDF

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