Download Presentation
## PARABOLIC MOTION

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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**Projectile motion**Horizontal component of velocity is constant over entire path! vx = v0x= v0cosa No acceleration in horizontal direction**Projectile motion**Vertical component of velocity constantly changing due to gravitational acceleration in -y direction v0y --> 0 -> -v0y v0y = v0sina**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 a= constant Dx = v0xt = (v0cos a)t**Projectile motion**Vertical motion of projectile: vy = v0sin a - gt Dy = (v0sin a)t - 1/2gt2 vy2 = (v0sin a)2 - 2gDy**Projectile motion**Combined 2D motion: v = (vx2 + vy2)1/2 tanq = vy/vx q = tan-1(vy/vx) -90 < q < 90**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:**• 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°