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Lesson Objectives

The student will:

• draw and interpret graphs involving two-dimensional projectile motion
• solve for the instantaneous velocity of a projectile
• predict a projectile’s range

Vocabulary

Free fall

The condition of acceleration which is due only to gravity.  An object in free fall is not being held up, pushed, or pulled by anything except its own weight.  Though objects moving in air experience some force from air resistance, this is sometimes small enough that it can be ignored and the object is considered to be in free fall. 

Projectile motion

Projectile motion is a form of motion where an object (called a projectile) is thrown near the earth's surface with some horizontal component to its velocity.  The projectile moves along a curved path under the action of gravity. The path followed by a projectile is called its trajectory. Projectile motion is motion in two directions. In the vertical direction, the motion is accelerated motion and in the horizontal direction, the motion is constant velocity motion.

Instantaneous velocity of a projectile

Instantaneous velocity is the velocity of an object at one instant during its motion. In the case of a projectile, the instantaneous velocity vector would be the resultant of a constant velocity horizontal motion and an accelerated velocity vertical motion.

Range

A projectile launched with specific initial conditions will travel a predictable horizontal displacement before striking the ground. This distance is referred to as the projectile's range.

Introduction

“Independence of Motion along Each Dimension” looks at the special case of throwing an object in a purely horizontal direction.  Projectile motion is the general case of throwing an object in any direction, from sliding an object off a desk to kicking a soccer ball as shown in the Figure below.

Components of Projectile Motion

In the problem that follows we imagine the projectile launched from the ground with an angular elevation between 0 and 90 degrees, with an initial x−component of velocity of +30 m/s and an initial y−component of velocity of +40 m/s.