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For this lab you will be looking at how the initial conditions for the projectile's flight influence its time in the air and its horizontal distance traveled.

Use the arrows at the bottom to adjust the speed, angle and height. Then estimate the landing location of the ball.

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For this lab you will be looking at how the initial conditions for the projectile's flight influence its time in the air and its horizontal distance traveled. Use the arrows at the bottom to adjust the speed, angle and height. Then estimate the landing location of the ball.

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This animation shows that horizontal and vertical velocities of a falling object are independent. The plane and the train are both moving with the same velocity when a ball is dropped from the plane. It carries on with the same horizontal velocity (ignoring air resistance) but accelerates downwards.

Press the START button to start.

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This animation shows that horizontal and vertical velocities of a falling object are independent. The plane and the train are both moving with the same velocity when a ball is dropped from the plane. It carries on with the same horizontal velocity (ignoring air resistance) but accelerates downwards.

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1. Open the simulation
2. choose your object from the right list
3. set your  initial speed
4. Hit the target ( Take a screenshot upload )

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Physics Lesson 9 Projectile Motion Intro (With StickMan Physics)

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About this Air Resistance Drag Parameter b/m ...

For a spherical projectile traveling through air, a reasonable approximation to the drag force is

where A is the area π r ² , ρ is the air density, v is the speed, and C D is the drag coefficient, often taken to be 0.5, based on experiment. The b is standard notation.

The coefficient C D is difficult to determine theoretically-trajectory predictions with air resistance are at best semi-quantitative. Experimentally, C D increases dramatically at velocities near the speed of sound (the "sound barrier") but then decreases again. So results at high velocities with a constant C D are not too reliable. (Our code could be modified to include a velocity-dependent drag, though.)

For ping pong balls, tennis balls and golf balls, the lift force from a high spin will also affect the results: we haven't tried to include that here.

Putting in the numbers (you should check!), we find for a tennis ball b/m is about 0.019, for a golf ball about 0.009, for a ping pong ball about 0.14.

For a cannonball, a Napoleon 12-pounder as used in the Civil War, we get b = 0.000033, but the initial speed is about 440 m/sec, supersonic, so the drag will be increased to well above the naïve formula. For modern artillery shells, b will be lower since they are not spherical, so the mass is greater than for a sphere presenting the same cross-sectional area perpendicular to the direction of flight.

Thanks to John Welch of Cabrillo College for pointing out some errors in earlier figures.

Exercises: Try plotting the range as a function of angle for a fixed initial speed. What angle gives the maximum range? Is this the same if there is air resistance?

Plot the maximum range as a function of initial speed.

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Today, reaching every student can feel out of reach. With MyLab and Mastering, you can connect with students meaningfully, even from a distance. Built for flexibility, these digital platforms let you create a course to best fit the unique needs of your curriculum and your students.

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Projectile Motion | Equations | Definition | Example