PHY 02 Lesson 7: Projectile Motion

Projectile Motion

An object thrown in a curved path with a gravitational field effect involves motion in two dimensions.

Projectile

is an object or body thrown with an initial velocity and whose motion is influenced by the pull of gravity

Trajectory

is the curved path of a projectile. It is principally determined by two types of motion: vertical and horizontal motions.

Height (y or h)

is the maximum vertical displacement of a projectile.

Range (x or d)

is the maximum horizontal displacement of a projectile.

45 degrees

it is the furthest downrange (x)

parabola

Neglecting air resistance, the path of a projectile is

free fall with an initial horizontal velocity

What makes up projectile motion

Ideal conditions

means "perfect or simple" we may ignore other factors that could affect the situation. Ignoring air resistance

Act independent of Each Otherf

X-Axis and Y-Axis Velocity

X-axis Velocity/Motion

It is not affected by the acceleration due to gravity. It is at a constant velocity

Y-axis Velocity/Motion

It is affected by the acceleration due to gravity

It is accelerated at 9.8 m/s² down (- 9.8 m/s² )• Slows down on the way up and speeds up on the way down.

X-Axis and Y-Axis Velocity Combined

Combined the motion follows an upside down U shape or Parabola

X-Axis velocity will remain constant and the Y-Axis Velocity will be Accelerated by Gravity

If a person threw a ball with an initial YAxis component of 30 m/s and an initial X component of 5 m/s.

At the top of the parabola, neither the object's velocity nor its acceleration is 0!

• Only Vyis 0

• Vxis constant throughout the flight

• Horizontal acceleration is always 0 m/s2

• Vertical acceleration is always -9.81 m/s2

Important Concepts for Projectiles Launched at an Angle

SOH CAH TOA

Use it to find the Vx,0 and Vy,0

• Use the Pythagorean theorem to find the resultant velocity using the components (Vx and Vy)

• Use SOH-CAH-TOA to find the direction.

Finding the total velocity

𝑽𝒚 = 𝒔𝒊𝒏𝜽𝑽↓𝟎

Y-component

𝑽𝒙 = 𝒄𝒐𝒔𝜽𝑽↓𝟎

X-component

𝐯𝐱

final horizontal velocity

𝐯𝟎𝐱

initial horizontal velocity

t

time to reach the highest pointor lowest point (depends on the case)

𝐯

final velocity

𝐯𝟎

initial velocity

∆y

height or vertical displacement

g

acceleration due to gravity(−9.8 𝑚⁄𝑠2)