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### Projectiles

### Projectiles Launched at an Angle level ground. The muzzle velocity of

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?

Homework - Page 99: 1-4 level ground. The muzzle velocity of

Physics 2010

Horizontal Component of Projectile Motion level ground. The muzzle velocity of

Vertical Component level ground. The muzzle velocity of of Projectile Motion

Projectile Launched at an Angle level ground. The muzzle velocity of

When launched at an angle… level ground. The muzzle velocity of

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… level ground. The muzzle velocity of

Initial velocity analysis:

V

Vyi = V sinθ

Vx = Vcosθ

These values can now be used in the kinematic equations…

Old Equations level ground. The muzzle velocity of

You kick a soccer ball at an angle of 40 level ground. The muzzle velocity of 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 level ground. The muzzle velocity of 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 level ground. The muzzle velocity of 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 level ground. The muzzle velocity of 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 an angle of 30.0 degrees above the horizontal. 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.

More Projectiles Launched at an Angle Practice an angle of 30.0 degrees above the horizontal.

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 30.0above the horizontal.

- Find the range of the projectile.

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