Chapter 3Projectile Motion

Projectile Motion

• Previously, we studied motion in one direction (linear motion)

• Projectiles follow a curved path (nonlinear motion)

The velocity of a projectile has both vertical and horizontal components to its motion that are independent of each other.

Vectors

• A scalar quantity has only magnitude Ex. 70 mph

• A vector quantity has both magnitude and directionEx. 70 mph, North

In physics an arrow is drawn to represent a vector. The length of the arrow is proportional to the magnitude of the vector and the arrow shows the direction.

Components of Vectors

• “Any vector can be “resolved” into two component vectors at right angles to each other. • “These two vectors are known as components of the given vector they replace.” - p. 31

80 km/hr

60 km/hr

Horizontal Distance

Verti

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ista

nce

• Each box represents one time interval (Ex. 1 sec)

• Purple dots represent the horizontal position (top), vertical position (left side) and position in space (curved line) of a projectile.

• Notice that the horizontal speed of the projectile remains constant

• The vertical speed of the projectile acts like an object in free-fall

• The only force acting on our projectile is gravity (neglecting air resistance)

Horizontal Distance

Verti

cal D

ista

nce

• The Horizontal Distance vs. time that a projectile will travel will be constant: Distance = Velocity x Time

• The vertical Distance vs time that a projectile will fall will follow the equation d=½gt2

(Note this applies only if a projectile is dropped from rest. If there is an initial velocity, we have to use the expanded equation:d= vit + ½gt2)

Example 1 • Suppose a ball is rolled off of a cliff horizontally with a speed of 5 m/s

• How long will it take the ball to hit the ground?

d=½gt2

123 = ½(9.81)(t2)t= 5s

• How fast was the ball traveling in the downward direction when it hit the ground?

v = gtv = (9.81)(5) = 49 m/s

• How fast in the horizontal direction was the ball traveling when it hit the ground? 5 m/s

• How far from the cliff will the ball land?

Distance = Velocity x TimeDistance = (5 m/s)(5s) = 25 meters

123 Meters