Projectiles

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# Projectiles - PowerPoint PPT Presentation

Projectiles. Physics 2010. Projectile Motion. Free-fall with an initial horizontal velocity (assuming we ignore any effects of air resistance) The curved path that an object follows when thrown or launched near the surface of Earth is called a trajectory. Projectiles.

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### Projectiles

Physics 2010

Projectile Motion
• Free-fall with an initial horizontal velocity

(assuming we ignore any effects of air resistance)

• The curved path that an object follows when thrown or launched near the surface of Earth is called a trajectory
Projectiles
• Any object that is thrown or launched into the air and are subject to gravity
• Projectiles follow perfect parabolic trajectories when air resistance is neglected
Horizontal Motion of a Projectile
• Constant when air resistance is negligible
• At any point in a projectile’s path, horizontal velocity is the same initial horizontal velocity
Vertical Motion of a Projectile
• Acceleration is a constant -9.81 m/s2
• At the peak of a projectile’s path, vertical velocity is zero
Projectile Motion
• The horizontal and vertical components of motion are completely independent of one another.
Sally throws a ball off the edge of a 15.0 m tall cliff. She throws it horizontally at 8.0 m/s.

a. Determine how much time it takes to fall.

Sally throws a ball off the edge of a 15.0 m tall cliff. She throws it horizontally at 8.0 m/s.

b. Determine how far from the base of the cliff it is when it hits the ground.

Sally throws a ball off the edge of a 15.0 m tall cliff. She throws it horizontally at 8.0 m/s.

c. Determine how fast it is moving vertically when it hits the ground.

Sally throws a ball off the edge of a 15.0 m tall cliff. She throws it horizontally at 8.0 m/s.

d. Determine what its total velocity is when it hits the ground.

A soccer ball is kicked horizontally off a 22.0 meter high hill and lands 35.0 m from the edge of the hill.
• Determine the initial horizontal velocity of the soccer ball.
A rifle is fired horizontally from a platform 10 m above level ground. The muzzle velocity of the gun is 500 m/s.
• How far downrange will the bullet hit the ground?

### Projectiles Launched at an Angle

Physics 2010

When launched at an angle…

The launch velocity of the projectile needs to be split up into its component parts for analysis purposes.

Note: the initial vertical velocity is no longer zero!!!

When launched at an angle…

Initial velocity analysis:

V

Vyi = V sinθ

Vx = Vcosθ

These values can now be used in the kinematic equations…

You kick a soccer ball at an angle of 40 above the ground with a velocity of 20.0 m/s.

a. How high will it go?

You kick a soccer ball at an angle of 40 above the ground with a velocity of 20.0 m/s.

b. How much time does it spend in the air?

You kick a soccer ball at an angle of 40 above the ground with a velocity of 20.0 m/s.

c. How far away from you will it hit the ground?

You kick a soccer ball at an angle of 40 above the ground with a velocity of 20.0 m/s.

d. What is the ball’s velocity when it hits the ground?

A golf ball is hit with a velocity of 24.5 m/s at 35.0 degrees above the horizontal.

a. Find the range of the ball.

A golf ball is hit with a velocity of 24.5 m/s at 35.0 degrees above the horizontal.

b. Find the maximum height of the ball.

A player kicks a football from ground level at 27.0 m/s at an angle of 30.0 degrees above the horizontal.

a. Find its “hang time” (time that the ball is in the air).

A player kicks a football from ground level at 27.0 m/s at an angle of 30.0 degrees above the horizontal.

b. Find the distance the ball travels before it hits the ground.

A player kicks a football from ground level at 27.0 m/s at an angle of 30.0 degrees above the horizontal.

c. Find its maximum height.

Example: You kick a soccer ball at an angle of 40 above the ground with a velocity of 20.0 m/s.
• One dimensional motion equations still apply.
• You will need to resolve the initial velocity into its x- and y-components to separate the horizontal from the vertical motion.
• Always keep the horizontal information separate from the vertical information in the problem.
An artillery shell is fired with an initial velocity of 100. m/s at an angle of 30.0 above the horizontal.
• Find its position and velocity after 8.00 s.
An artillery shell is fired with an initial velocity of 100. m/s at an angle of 30.0 above the horizontal.
• Find the time required to reach its maximum height.
An artillery shell is fired with an initial velocity of 100. m/s at an angle of 30.0above the horizontal.
• Find the range of the projectile.