Chapter 4: Two-Dimensional Kinematics Reference Tools & Resources

Reference Tools & Resources

I. Key Terms and Phrases

projectile motion: the motion of an object that is projected with an initial velocity and then moves under the influence of gravity only.

launch angle: the angle of the initial velocity of a projectile measured relative to the horizontal.

range: the horizontal distance traveled by a projectile before it lands.

II. Important Equations

Name/Topic	Equation	Explanation
constant velocity	x = x0 + v0xt y = y0 + v0yt	Each direction obeys the constant velocity equation independently.
constant acceleration: horizontal component	vx = v0x + axt	The constant acceleration equations for horizontal components.
constant acceleration: vertical component	vy = v0y + aat	The constant acceleration equations for vertical components.
range of a projectile		The horizontal distance traveled if the initial height equals the final height.
time-of-flight of projectile		The total time in the air if the initial height equals the final height
maximum height of a projectile		The maximum height above the initial height of launch

III. Other Useful Tips

As discussed in chapter two, you may find it useful to add a fifth equation to the list of equations describing motion with constant acceleration. This equation does not contain the initial velocity. In the context of two-dimensional motion the additional equations would be

or, in the context of projectile motion

.

In addition to the equations derived in your text and listed below for projectile motion, it may also be useful to know the equation for the path of the projectile, that is, y as a function of x. This result can be determined by solving for t from the horizontal equation, x - x₀ = (v₀ cosq)t, and substituting this into the vertical equation . After some manipulations the result is

.

Try to rework Example 4.4 using this equation.

Reference Tools and Resources by David Reid, Eastern Michigan University. ©2002 by Prentice Hall, Inc.

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