Gravity and Projectiles Acceleration of Gravity Loses speed for each interval of time it rises on an upward throw Gains at same rate on its downward path 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 gravity Distance 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 gravity Types of Motion Linear in a straight line Non linear curved path Projectiles have curved path called parabola Parabolic curves are parabolas Projectiles Move both horizontally and vertically Vertical motion influenced by gravity Horizontal motion not influenced by gravity Are NOT dependent upon one another Roll the Ball Freely falling object Has acceleration downward Pushed away from table Has velocity outward Combines to have a parabolic path Photo of ball falling http galileo rice edu lib student work experiment95 paraintr html Path of Ball from Side Ball Rolling off table ho rizo nt al Top View of the ball Top View Series2 distance from table Front View the ball Front View Projectile motion Each component acts separately Same horizontal distance in each time increment Vertical distance increases for each time increment that passes What 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 gravity http www physicsclassroom com Class vectors U3L2a html There is gravity This is the outside force acting on the object to change its course Components of cannonball motion http www physicsclassroom com Class vectors u3l2b html Cannonball with gravity http www physicsclassroom com mmedia vectors hlp gif Airplane 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 gif Airplane and Package a b c d 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 Straight down from where it was dropped Underneath plane 80 m behind plane More than 120 m behind plane Airplane 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 gif Cannon Ball Trajectory Cannonball without gravity with no Gravity 350 300 Vertical height 250 200 150 100 50 0 0 50 100 150 200 250 Horizontal distance 300 350 Faster Cannonball Cannonball with gravity 350 300 H eig h t 250 200 150 100 50 0 0 50 100 150 200 Distance 250 300 350 Banana without gravity http www physicsclassroom com mmedia vectors mzng gif Banana with gravity http www physicsclassroom com mmedia vectors mzg gif Slower banana http www physicsclassroom com mmedia vectors mzs html Cannon Ball Trajectory with no Gravity 350 300 Vertical height 250 200 150 100 50 0 0 50 100 150 200 250 Horizontal distance 300 350 Cannonball with Gravity 90 80 V ertical H eig h t 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 Horizontal Distance Cannonball with gravity Vectors of projectile motion Steeper trajectory Acceleration of Cannonball What is the acceleration in a horizontal direction What is the acceleration in a vertical direction Cannonball 90 80 70 V e r t ic a l 60 50 40 30 20 10 0 0 10 20 30 40 50 Horizontal 60 70 80 90 Steeper Cannonball 350 300 Vertical 250 200 150 100 50 0 0 50 100 150 200 Horizontal 250 300 350 Projectile Range http www physicsclassroom com mmedia vectors mr gif Cannonball Trajectories Cannonball 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 down With air resistance Calculations of distance speed and acceleration How fast was this ball thrown How fast was ball thrown Want to find dhorz t We can calculate t dvert gt2 We know dhorz dvert g How fast was ball thrown dvert gt2 dvert 5 m g 10 m s2 Solve for how long to fall 1 2 d gt 2 5m 2 t 1 10m 2 2 s 1 10m 2 5m 2 t 2 s t 5m 1s 1 10m 2 2 s 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 s How fast was ball thrown v 20m 1s 20 m s 72 5 mi h 20m 60 s 60 min 1km 0 62mi 44 6mi h s min h 1000m 1km Object thrown horizontally Falls the same distance in the same time no matter the speed of the throw Satellite as projectile No gravity No gravity http www physicsclassroom com mmedia vectors tp gif Satellite as projectile 6000 m s 6000 m s http www physicsclassroom com mmedia vectors 6kms gif Satellite as projectile 8000 m s 8000 m s http www physicsclassroom com mmedia vectors co gif Object 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 path Acceleration of Gravity Free fall of object Time elapsed Speed increases seconds 10 m s for every second of fall 0 10 m s 10m 1 s s2 2 Speed meters second 0 10 20 3 30 4 40 Speed and distance of falling objects Remember that velocity is defined as distance time Average velocity can be determined over time intervals average velocity v2 v1 2 Speed Time elapsed meters second secon ds 0 0 1 10 2 20 3 30 4 40 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 objects v a t at v gt v Freely falling object Velocity is a function of how long it has been falling Distance is also a function of how long it has been falling because And average velocity is …
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