Unit 3.1 Projectile Motion · 2007-12-08 · •Projectiles –Falling –Falling with an initial horizontal velocity Falling Objects •All objects close to the surface of the earth

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Unit 3.1 Projectile Motion

Teacher: Dr. Van Der Sluys

Objectives

• Two dimensional motion– Vertical– Horizontal

• Projectiles– Falling– Falling with an initial horizontal velocity

Falling Objects

• All objects close to the surface of theearth will fall due to gravity with anacceleration of -9.8 m/s2

• This acceleration only occurs in thevertical direction and is independentupon motion in the horizontal direction.

• The horizontal velocity of a fallingobject will remain constant.

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Falling Versus Projectiles

The Equations

d = Vit + 1/2at2

a = (Vf - Vi)/t

Vf2 = Vi

2 + 2 ad

Get organized: Create A Table

d =d =

t =t =

Vf =Vf =

Vi =Vi =

a = -9.8 m/s2a = 0 m/s2

VerticalHorizontal

Note: tvertical = thorizontal

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Strategy

• Insert any given and known/assumedinformation into the table.

• Solve for the variables that are notknown using the appropriate equations.

• Don’t confuse the variables in thevertical and horizontal

Problem

• If an object rolls off a table that is 0.75m tall with a horizontal velocity of +2.0m/s, how far from the base of the tablewill the object hit the floor?

The Effect of ChangingInitial Velocity

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Launching Projectiles at Angles

Problem

• If a projectile is launched at an angle of30° above the horizontal with muzzlevelocity of 200 m/s, what are thevertical and horizontal components ofthis vector?

Answer: X = 173 m/s; Y = 100 m/s

Problem

• If a projectile is launched at an angle of30° above the horizontal with a muzzlevelocity of 200 m/s, how long will theobject be in the air if it hits the groundat the same height at which it waslaunched?

Answer: 20.4 s

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Problem

• If a projectile is launched at an angle of30° above the horizontal with a muzzlevelocity of 200 m/s, how far will theobject travel horizontally if it lands atthe same height as it was launched?

Answer: 3.53 x 103 m

Projectile Problem Solving

1. Determine the horizontal (Vx) and vertical(Vy) components of the initial muzzlevelocity.

2. Determine the time the object will be in theair based on

a = (Vof - Voi)/t or d = Voyt + 1/2 at2a = -9.8 m/s2

3. Determine the distance the projectile willtravel horizontally using dx = Vixt

What is the Range of aProjectile

• How far will a projectile travelhorizontally if it is fired with a muzzlevelocity of 250 m/s at an angle of 45°above the horizontal?

Answer: 6390 m