Introduction to Projectile Motion Learning Goal: To understand the basic concept

Question

Introduction to Projectile Motion

Learning Goal:

To understand the basic concepts of projectile motion.

Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really little different from the one-dimensional motions that you may already have studied.

One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity v? . In general, this velocity can point in any direction in the xy plane and can have any magnitude. To make a problem more manageable, it is common to break up such a quantity into its x component v?x and its y component v?y .

Consider a particle with initial velocity v? that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis.

Part A

What is the x component v?x of v? ?

Express your answer in meters per second.

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Part B

What is the y component v?y of v? ?

Express your answer in meters per second.

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Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not.

Part C

Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle's shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components?

Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle's shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components?

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Part D

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Part E

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Introduction to Projectile Motion

Learning Goal:

To understand the basic concepts of projectile motion.

Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really little different from the one-dimensional motions that you may already have studied.

One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity v? . In general, this velocity can point in any direction in the xy plane and can have any magnitude. To make a problem more manageable, it is common to break up such a quantity into its x component v?x and its y component v?y .

Consider a particle with initial velocity v? that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis.

Part A

What is the x component v?x of v? ?

Express your answer in meters per second.

SubmitHintsMy AnswersGive UpReview Part

Part B

What is the y component v?y of v? ?

Express your answer in meters per second.

vx = m/s

SubmitHintsMy AnswersGive UpReview Part

Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not.

Part C

Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle's shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components?

Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle's shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components?

vy = m/s

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Part D

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Part E

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Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both the vertical and horizontal components exhibit motion with constant velocity.

Explanation / Answer

Consider a particle with initial velocity that has magnitude 12.0 m/s and is directed 60° above the negative x axis.

V = 12.0 m/s angle 60° above x axis

Vx/V = -cos 60

Vx = -Vcos60 = -0.5*V = -6.0 m/s (I took positive x as positive velocity)

Vy/V = sin 60

Vy = Vsin60 = 12.0 * 0.8660 = 10.4 m/s

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