Parabolic motion

PARABOLIC MOTION

Created by Dr. Eng. Supriyanto, M.Sc Slide - 1
Fundamental of Physics http://supriyanto.fisika.ui.edu

Describing parabolic motion

Parabolic motion refers to the motion of an object
that is thrown, or projected, into the air at an angle.

Parabolic motion is a combination of horizontal motion
with constant horizontal velocity and vertical motion
with a constant downward acceleration due to gravity.

The vertical motion of a projected object is independent of
its horizontal motion.

The one common variable between
the horizontal and vertical motions is time.

Parabolic motion

Velocities vector of
horizontal
and vertical motion


Parabolic motion

 Horizontal
 Motion of a ball rolling freely along a
level surface
 Horizontal velocity is ALWAYS constant

Vertical
 Motion of a freely falling object
 Force due to gravity
 Vertical component of velocity changes
with time
 Parabolic
 Path traced by an object accelerating
only in the vertical direction while
moving at constant horizontal velocity


Parabolic motion

Horizontal
and vertical motion


Parabolic motion

Time of flight
is determined
by
vertical motion


The bullet motion


Angle for maximum distance


Projectile motion

Horizontal component of velocity is constant over entire path!
vx = v0x= v0cosα
No acceleration in horizontal direction

Projectile motion

Vertical component of velocity constantly changing due to
gravitational acceleration in -y direction
v0y --> 0 -> -v0y v0y = v0sinα

Projectile motion

At the top of the trajectory:
t = 1/2 of total time
x = 1/2 of total horizontal range

Projectile motion

Horizontal motion of projectile:

vx = v0cos α = constant
∆x = v0xt = (v0cos α)t


Projectile motion

Vertical motion of projectile:

vy = v0sin α - gt
∆y = (v0sin α)t - 1/2gt2
vy2 = (v0sin α)2 - 2g∆y


Projectile motion

Combined 2D motion:

v = (vx2 + vy2)1/2
tanθ = vy/vx
θ = tan-1(vy/vx)
-90 < θ < 90


Simulation#1


Simulation#2


Simulation#3


Exercise#1


Summary

• A projectile is a body in free fall that is affect only by
gravity and air resistance.
• Projectile motion is analyzed in terms of its horizontal and
vertical components.
Vertical is affect by gravity
• Factors that determine the height & distance of a projectile
are; projection angle, projection speed, and relative
projection height
• The equation constant acceleration can be used to
quantitatively analyze projectile motion.


Exercise #2:

1. A batter hits a ball at 35 with a velocity of 32 m/s.
How high did the ball go?
H = 17 m
How long was the ball in the air?
t = 3.8 s
How far did the ball go?
x = 98 m


Exercise #2:

2. While driving down a road a bad guy shoots a bullet
straight up into the air. If there was no air resistance
where would the bullet land – in front, behind, or on him?

• If air resistance present, bullet slows and lands behind.
• No air resistance, the Vx doesn’t change and bullet lands
on him.


Exercise #2:

3. A truck (v = 11.2 m/s) turned a corner too sharp and lost
part of the load. A falling box will break if it hits the
ground with a velocity greater than 15 m/s. The height of
the truck bed is 1.5 m. Will the box break?

v = 12 m/s, No it doesn’t break


Exercise #2:

4. A meatball with v = 5.0 m/s rolls off a 1.0 m high table.
How long does it take to hit the floor?
t = 0.45 s
What was the velocity when it hit?
v = 6.7 m/s @ 42°


Parabolic motion

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Parabolic motion