Types of Motion. Photo of ball falling

Transcription

1 Gravity an Projectiles Acceleration of Gravity Loses spee for each interval of time it rises on an upwar throw Gains at same rate on its ownwar path Upwar motion Acte upon by gravity, just like a falling object Goes up slower an slower, until upwar velocity reaches zero Goes shorter an shorter istances in same time interval Slows at m/s, the acceleration of gravity Distance, velocity, time of upwar-moving object Velocity at position on the way up is the same as velocity in the same position on the way own (neglecting air resistance) Velocity reaches zero, object begins to fall Then is falling uner the influence of gravity Types of Motion Linear in a straight line Non-linear curve path Projectiles have curve path calle parabola Parabolic curves are parabolas Projectiles Move both horizontally an vertically Vertical motion influence by gravity Horizontal motion not influence by gravity Are NOT epenent upon one another Roll the Ball Freely falling object Has acceleration ownwar Pushe away from table Has velocity outwar Combines to have a parabolic path Photo of ball falling Path of Ball from Sie Ball Rolling off table horizont al

2 Top View of the ball Front View Front the ball Projectile motion Top View Series Each component acts separately Same horizontal istance in each time increment Vertical istance increases for each time increment that passes istance from table What if?? What if you roppe a cannon ball off the cliff at exactly the instant a cannon was fire in the horizontal irection? Which cannon ball woul hit the groun first? Cannonball without gravity There is gravity This is the outsie force acting on the object to change its course Components of cannonball motion Cannonball with gravity Airplane an Package Flying straight an level at 45 m above groun level, at a spee of 4 m/s Drops package, which falls to the groun Where will package lan? (neglect air resistance)

3 Airplane an Package Flying straight an level at 45 m above groun level, at a spee of 4 m/s Drops package, which falls to the groun Where will package lan? (neglect air resistance) a) Straight own from where it was roppe b) Unerneath plane c) 8 m behin plane ) More than m behin plane Airplane an Package Flying straight an level at 45 m above groun level, at a spee of 4 m/s Drops package, which falls to the groun Where will package lan? (neglect air resistance) Vertical height Cannon Ball Trajectory with no Gravity Cannonball without gravity Horizontal istance 35 Cannonball Faster Cannonball with gravity Banana without gravity Banana with gravity 3 5 Height Distance Slower banana Cannon Ball Trajectory with no Gravity 9 Cannonball with Gravity 8 7 Vertical height Vertical Height Horizontal istance Horizontal Distance Cannonball with gravity 3

4 Vectors of projectile motion Steeper trajectory Acceleration of Cannonball What is the acceleration in a horizontal irection? Cannonball What is the acceleration in a vertical irection? Vertical Horizontal 35 Steeper Cannonball Projectile Range Cannonball Trajectories 3 5 Vertical Horizontal 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 spee on the way own With air resistance Calculations of istance, spee an acceleration How fast was this ball thrown? 4

5 How fast was ball thrown? Want to fin horz /t, We can calculate t vert = (½) gt, We know horz, vert, g How fast was ball thrown? vert = (½) gt vert, = 5 m g = m/s Solve for how long to fall m = gt 5m = ( ) t s 5m t = m ( ) s 5m t = = s m ( ) s How fast was ball thrown? Want to fin v v = horz /t We calculate t = s Distance= m v = m/ s v= m/s How fast was ball thrown? v = m/s = m/s (7.5 mi/h) m 6s 6 min km.6mi = 44.6mi / h s min h m km Object thrown horizontally Falls the same istance in the same time, no matter the spee of the throw No gravity Satellite as projectile 6 m/s Satellite as projectile 8 m/s Satellite as projectile No gravity 6 m/s 8 m/s 5

6 Object thrown horizontally Falls the same istance in the same time, no matter the spee of the throw Earth s surface is 5 meters lower for every 8 meters horizontal istance Earth s surface is 5 meters lower for every 8 meters horizontal istance If it is thrown 8m/s, it will never reach the surface Because it falls just as fast as the surface eparts from a horizontal path If it is thrown 8m/s, it will never reach the surface (nearly 8, mi/h) Because it falls as fast as the surface eparts from a horizontal path Acceleration of Gravity Free fall of object Spee increases m/s for every secon of fall m/s = m s s Time elapse (secons) 3 4 Spee (meters/ secon) 3 4 Spee an istance of falling objects Remember that velocity is efine as istance / time Average velocity can be etermine over time intervals average velocity= v + v Time elapse (secon s) 3 4 Spee (meters/ secon) 3 4 Acceleration an falling objects Remember that acceleration is efine as change of velocity / time Which can be rearrange to report velocity An we use the acceleration of gravity for freely falling objects a = Δv t at = Δv gt = Δv 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 An average velocity is sum of two velocities ivie by gt = Δv vt = v + v Freely falling objects We will use this equation An substitute average velocity calculate from two velocities Which will be calculate from v average vt = v v = + gt = v Freely falling objects So the master equation Substitute the average velocity Substitute the velocity calculate from the acceleration of gravity An remember the object starts at rest vt = v gt = + v v t = + gt t = 6

7 v = v =gt Distance of falling object Now we have: Which simplifies to: + gt t = gt t = gt = Time of falling object gt = An if you know the istance you can gt = calculate the time it has fallen gt = Multiply both sies by gt Divie both sies by g = t = Take square root of g g g both sies to get time: t = t = g Hang time for basketball player Spu Webb slam unk contest He can jump.5 m. How long is he in the air? = gt t = (.5m) t = = =. 5s g m / s g to fall from top of jump, so ouble for time in the air 7