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Projectile Motion. Or “Fly me to the Moon”. Projectile. A projectile is an object that once given an initial velocity moves only under the influence of gravity. Examples: bullets, baseballs, cannonballs, divers, golf balls, basketballs, volleyballs, footballs, fountains, car flying off cliff

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## Projectile Motion

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**Projectile Motion**Or “Fly me to the Moon”**Projectile**• A projectile is an object that once given an initial velocity moves only under the influence of gravity. • Examples: bullets, baseballs, cannonballs, divers, golf balls, basketballs, volleyballs, footballs, fountains, car flying off cliff • Anti-examples: Rockets when engines are on, airplanes when under power, car on road • all have force acting besides gravity**Perpendicular Motion Vectors are Independent**• The horizontal motion of a projectile does not effect the vertical motion of the same projectile. • Examples • 2D apparatus demo • Two bullet problem**Horizontal Projectile**• Horizontal motion is one of constant speed • DD=v0Dt • Vf=v0 • A=0 • Vertical motion is one of freefall • DD=1/2 ag Dt2 • Vf=ag Dt • Ag=-10m/s/s**Check Question 1**• A cannon sits on a 80 m high cliff. If a cannon ball is projected horizontally with an initial velocity of 10 m/s answer the following questions. • What are the horizontal speed and distance traveled of the ball after 3 seconds? • What are the vertical speed and distance traveled of the ball after 3 seconds? • When does the ball hit the ground? • How far away from the cliff does the ball hit?**Projectiles Launched at Angles**• Decompose initial velocity vector • Vertical equations • DDy=v0yt + 1/2 ag Dt2 • Vfy=v0y+ag Dt • Vfy 2=v0y 2+2agDdy • (vfy +v0y) / 2 =Ddy • Horizontal Equation • Ddx=v0xDt • At top Vy=0, Vx=Vox, a= -10 m/s/s, max range at 45 degrees**The Monkey Shot**• If monkey does not let go then need to aim above monkey. • If monkey lets go at same time as bullet shot then aim directly at monkey • Bullet and monkey will fall at same rate • Bullet will fall off straight line no gravity path**Summary Slide**• Projectiles are objects which once given an initial velocity move under the influence of gravity only (neglecting air resistance). • The vertical and horizontal components of motion are independent of one another. • The horizontal motion of a projectile is that of an object with a constant speed. The vertical motion is that of an object undergoing a constant acceleration.**Upward Projected Object**• Decompose initial velocity • Horizontal motion is constant velocity. • D=v0xDt, a=0 • Vf=v0x • Vertical motion is difference between motion due to initial speed and freefall • DDy=v0y Dt - 1/2 ag Dt2 • Vfy=v0y-ag Dt • Vfy 2=v0y 2-2agDdy • (vfy +v0y) Dt / 2 =Ddy**Downward Projected Object**• Horizontal motion is that of object moving with constant velocity • D=v0x t a=0 • Vf=v0x • Vertical motion is sum of motion due to initial velocity and freefall • D=-v0yt - 1/2 agt2 • Vfy=-v0y-agt • a=10m/s/s

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