Gravity and ProjectilesAcceleration of GravitySpeed and distance of falling objectsAcceleration and falling objectsFreely falling objectFreely falling objectsFreely falling objectsDistance of falling objectTime of falling objectHang time for basketball player1Gravity and ProjectilesAcceleration of Gravity• Free fall of object• Speed increases 10 m/s for every second of fall• 10 m/s= 10mss2Time elapsed(seconds)Speed (meters/ second)00 110220330440Speed and distance of falling objects• Remember that velocity is defined as distance / time• Average velocity can be determined over time intervals• average velocity=Time elapsed(seconds)Speed (meters/ second)00 1102203304402vv12+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=vat Δ=vgt Δ=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 sum of two velocities divided by 2vgtΔ=dvt =2vv12+Freely falling objects• We will use this equation• And substitute average velocity calculated from two velocities• Which will be calculated from dvt =2vv12+=averagevvgt=2Freely falling objects• So the master equation• Substitute the average velocity• Substitute the velocity calculated from the acceleration of gravity• And remember the object starts at rest vgt=dvt =dt =+2vv10dtgt=⋅+20Distance of falling object•v1=0•v2=gt• Now we have:• Which simplifies to:dtgt=⋅+20dtgt=⋅2dgt =221Time of falling object• And if you know the distance…you can calculate the time it has fallen• Multiply both sides by 2• Divide both sides by g• Take square root of both sides to get time:dgt =221dgt ⋅=⋅ 22122dgt ⋅= 22gdggt ⋅=22gdt⋅=22gdtt⋅==22Hang time for basketball player• Spud Webb slam dunk contest• He can jump 1.25 m. How long is he in the air?→to fall from top of jump, so double for time in the airgdt2=• http://www.youtube.com/watch?v=BUu7drj9hPw221gtd =ssmmgdt
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