1Gravity and Projectiles• Loses speed for each interval of time it rises on an upward throw• Gains at same rate on its downward pathAcceleration of Gravity Upward motion• Acted upon by gravity, just like a falling object• Goes up slower and slower, until upward velocity reaches zero• Goes shorter and shorter distances in same time interval• Slows at 10 m/s2, the acceleration of gravityDistance, velocity, time of upward-moving object• Velocity at position on the way up is the same as velocity in the same position on the way down (neglecting air resistance)• Velocity reaches zero, object begins to fall• Then is falling under the influence of gravityTypes of Motion• Linear—in a straight line• Non-linear—curved path• Projectiles have curved path called “parabola”• Parabolic curves are parabolasProjectiles• Move both horizontally and vertically• Vertical motion influenced by gravity• Horizontal motion not influenced by gravity• Are NOT dependent upon one anotherRoll the Ball• Freely falling object– Has acceleration downward• Pushed away from table– Has velocity outward• Combines to have a parabolic pathPhoto of ball fallinghttp://galileo.rice.edu/lib/student_work/experiment95/paraintr.htmlPath of Ball from SideBall Rolling off tablehoriz ont al2Top View of the ballTop Viewdista nce from tabl eSeries2Front View the ballFront ViewProjectile motion• Each component acts separately• Same horizontal distance in each time increment• Vertical distance increases for each time increment that passesWhat if??• What if you dropped a cannon ball off the cliff at exactly the instant a cannon was fired in the horizontal direction?• Which cannon ball would hit the ground first?Cannonball without gravityhttp://www.physicsclassroom.com/Class/vectors/U3L2a.htmlThere is gravity• This is the outside force acting on the object to change its courseComponents of cannonball motionhttp://www.physicsclassroom.com/Class/vectors/u3l2b.htmlCannonball with gravityhttp://www.physicsclassroom.com/mmedia/vectors/hlp.gifAirplane and Package• Flying straight and level at 45 m above ground level, at a speed of 40 m/s• Drops package, which falls to the ground• Where will package land? (neglect air resistance)http://www.physicsclassroom.com/mmedia/vectors/pap.gif3Airplane and Package• Flying straight and level at 45 m above ground level, at a speed of 40 m/s• Drops package, which falls to the ground• Where will package land? (neglect air resistance)a) Straight down from where it was droppedb) Underneath planec) 80 m behind planed) More than 120 m behind planeAirplane and Package• Flying straight and level at 45 m above ground level, at a speed of 40 m/s• Drops package, which falls to the ground• Where will package land? (neglect air resistance)http://www.physicsclassroom.com/mmedia/vectors/pap.gifCannon Ball Trajectory with no Gravity0501001502002503003500 50 100 150 200 250 300 350Horizontal distanceVertical heightCannonball without gravityFaster Cannonball0501001502002503003500 50 100 150 200 250 300 350DistanceHeightCannonball with gravityBanana without gravityhttp://www.physicsclassroom.com/mmedia/vectors/mzng.gifBanana with gravityhttp://www.physicsclassroom.com/mmedia/vectors/mzg.gifSlower bananahttp://www.physicsclassroom.com/mmedia/vectors/mzs.htmlCannon Ball Trajectory with no Gravity0501001502002503003500 50 100 150 200 250 300 350Horizontal distanceVertical heightCannonball with Gravity01020304050607080900 102030405060708090Horizontal DistanceVertical HeightCannonball with gravity4Vectors of projectile motion Steeper trajectoryCannonball01020304050607080900 10203040506070 8090HorizontalVerticalAcceleration of Cannonball• What is the acceleration in a horizontal direction?• What is the acceleration in a vertical direction?Steeper Cannonball0501001502002503003500 50 100 150 200 250 300 350HorizontalVerticalProjectile Rangehttp://www.physicsclassroom.com/mmedia/vectors/mr.gifCannonball TrajectoriesCannonball trajectories• Projectile will fall from maximum height in same amount of time it took to rise• Because the acceleration of gravity slows it at the same rate it increases the speed on the way downWith air resistanceCalculations of distance, speed and accelerationHow fast was this ball thrown?5How fast was ball thrown?• Want to find dhorz/t, • We can calculate t•dvert= (½) gt2, • We know dhorz, dvert, gHow fast was ball thrown?•dvert= (½) gt2•dvert, = 5 m• g = 10 m/s2Solve for how long to fall)10(21522smmt =22)10(215 tsmm =221gtd =ssmmt 1)10(2152==How fast was ball thrown?• Want to find v •v = dhorz/t• We calculated t = 1s• Distance=20 m• v = 20 m/1 s v=20 m/sHow fast was ball thrown?• v = 20m/1s = 20 m/s • (72.5 mi/h)hmikmmimkmhssm/6.44162.010001min60min6020=⋅⋅⋅⋅Object thrown horizontally• Falls the same distance in the same time, no matter the speed of the throwSatellite as projectileNo gravityNo gravity http://www.physicsclassroom.com/mmedia/vectors/tp.gifSatellite as projectile6000 m/s6000 m/s http://www.physicsclassroom.com/mmedia/vectors/6kms.gifSatellite as projectile8000 m/s8000 m/s http://www.physicsclassroom.com/mmedia/vectors/co.gif6Object thrown horizontally• Falls the same distance in the same time, no matter the speed of the throw• Earth’s surface is 5 meters lower for every 8000 meters horizontal distance• Earth’s surface is 5 meters lower for every 8000 meters horizontal distance• If it is thrown 8000m/s, it will never reach the surface• Because it falls just as fast as the surface departs from a horizontal path• If it is thrown 8000m/s, it will never reach the surface (nearly 18,000 mi/h)• Because it falls as fast as the surface departs from a horizontal pathAcceleration of Gravity• Free fall of object• Speed increases 10 m/s for every second of fall• 10 m/s= 10mss24043032021010 0Speed (meters/ second)Time elapsed(seconds)Speed and distance of falling objects• Remember that velocity is defined as distance / time• Average velocity can be determined over time intervals• average velocity=4043032021010 0Speed (meters/ second)Time elapsed(seconds)2vv12+Acceleration and falling objects• Remember that acceleration is defined as change of velocity / time• Which can be rearranged to report velocity• And we use the acceleration of gravity for freely falling objectstvaΔ=vatΔ=vgtΔ=Freely falling object• Velocity is a function of how
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