Parabolic motion

Slide - Slide - 11Fundamental of PhysicsFundamental of Physics Created by Dr. Eng. Supriyanto, M.Schttp://supriyanto.fisika.ui.edu

PARABOLIC MOTION


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

Describing parabolic motion

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.


Velocities vector ofhorizontal

and vertical motion

Parabolic motion


Parabolic motion

HorizontalHorizontal Motion of a ball rolling freely along a

level surface Horizontal velocity is ALWAYS

constant VerticalVertical

Motion of a freely falling object Force due to gravity Vertical component of velocity

changes with time ParabolicParabolic

Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity


Horizontal and vertical motion

Parabolic motion


Time of flightis

determined

byvertical motion

Parabolic motion


The bullet motion


Angle for maximum distance


Angle for maximum distance


Projectile motion

Horizontal component of velocity is constant over entire path!

vx = v0x= v0cosNo acceleration in horizontal direction


Projectile motion

Vertical component of velocity constantly changing due to gravitational acceleration in -y

directionv0y --> 0 -> -v0y v0y = v0sin


Projectile motion

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


Projectile motion

vx = v0cos = constantx = v0xt = (v0cos t

Horizontal motion of projectile:


Projectile motion

Vertical motion of projectile:

vy = v0sin - gty = (v0sint - 1/2gt2

vy2 = (v0sin2 - 2gy


Projectile motion

Combined 2D motion:

v = (vx2 + vy

2)1/2

tan = vy/vx

= tan-1(vy/vx)-90 < < 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 mHow long was the ball in the air?

t = 3.8 sHow 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°

Technology

Parabolic motion