Acceleration of Gravity Gravity and Projectiles 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 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 2 gt v vt d v2 v1 2 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 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 t a at v gt v Freely falling objects We will use this equation And substitute average velocity calculated from two velocities Which will be calculated from vt d vaverage v2 v1 2 gt v 1 Freely 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 Distance of falling object vt d v0 v1 t d 2 0 gt t d 2 gt t d 2 v1 0 v2 gt Now we have gt v 0 gt t d 2 1 2 gt d 2 Time of falling object And if you know the 1 distance you can 2 2 calculate the time it has fallen Multiply both sides by 2 gt 2 Divide both sides by g g Take square root of both sides to get time gt 2 2 d t gt 2 2 d Which simplifies to Hang time for basketball player Spud Webb slam dunk contest http www youtube com watch v BUu7drj9hPw He can jump 1 25 m How long is he in the air d 2 d 2 2 d t g g t2 2 d g 1 2 gt d 2 t 1 2 gt 2 t 2d 2 1 25m 0 5s g 10m s 2 2d g to fall from top of jump so double for time in the air 2
View Full Document
Unlocking...