 # Projectile Motion Previously, we studied motion in one direction (linear motion) Projectiles follow a curved path (nonlinear motion) The velocity of a.

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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 direction Ex. 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 Vertical Distance 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 Vertical Distance 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=½gt 2 (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= v i t + ½gt 2 )

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=½gt 2 123 = ½(9.81)(t 2 ) t= 5s How fast was the ball traveling in the downward direction when it hit the ground? v = gt v = (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 Time Distance = (5 m/s)(5s) = 25 meters 123 Meters

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