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PARABOLIC MOTION

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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.

- 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

Horizontal component of velocity is constant over entire path!

vx = v0x= v0cosa

No acceleration in horizontal direction

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

v0y --> 0 -> -v0y v0y = v0sina

At the top of the trajectory:

t = 1/2 of total time

x = 1/2 of total horizontal range

Vertical motion of projectile:

vy = v0sin a - gt

Dy = (v0sin a)t - 1/2gt2

vy2 = (v0sin a)2 - 2gDy

- 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.

- 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

- 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.

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

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°