Free Fall Projectile Motion free fall but not

Free Fall

Projectile Motion – free fall, but not vertical

Free Fall: • Used to describe the motion of any object that freely through a vacuum. is moving _______________ gravity • the only force acting is ________ air resistance • no ___________ , which is a good slowly approximation if object moves ______ up or down • motion can be _________ or in an arc parabola known as a __________ mass • the results are independent of ______ • All of the equations of _________can kinematics used as long as you use: -9. 81 m/s 2 a = ____________ -g = __________= 9. 81 m/s 2 down constant = _______on or near Earth’s surface free fall for the time the object is in ________.

Free fall applies to an object that is… dropped ______ from rest: thrown _____ down: fired up or at down _____ an angle _____: fired _______up: horizontally _______: in flight …only for the time while it is ________. In all cases: 1. d is _________if the object ends up positive above _____ the point where it started. 2. d is _________if the object ends up negative below _____ the point where it started. up or right 3. v is positive if object is going ________ down or left 4. v is negative if object is going ________ always -9. 81 m/s 2 5. a is _____________

Vertical I. _______ motion A. Dropped Objects. Ex 1: A ball is dropped. How far will it fall in 3. 5 seconds? equation: given: 2 d = v t + ½ at 2 i a = -9. 81 m/s vi = 0 d = 0 t + ½(-9. 81)(3. 5)2 t = 3. 5 s d = ½(-9. 81)(12. 25) unknown: d= ? d = -60. m

Ex. Harry Potter falls freely 99 meters from rest. How much time will he be in the air? given: a = -9. 81 m/s 2 equation: d = vit + ½ at 2 vi = 0 -99 = 0 t + ½(-9. 81)(t)2 d = -99 m -99 = -4. 905 t 2 unknown: t= ? t 2 = 20. 2 t = 4. 5 s

Ex. Mr. Siudy falls off a cliff. What will be his velocity at the instant he hits ground if he falls for 1. 3 seconds? equation: given: a = -9. 81 m/s 2 v = v + at f i v =0 i t= 1. 3 s unknown: vf = 0 + (-9. 81)(1. 3) vf = ? vf = -13 m/s A rock that has half the mass of Mr. Siudy is dropped at the same time. If it falls for the same time, what will its final speed be? Which will hit the ground first? same neither

B. Objects Fired Up or Down. Ex. A ball is tossed up with an initial speed of 24 meters per second. How high up will it go? vf given: a = -9. 81 m/s 2 vi = 24 m/s vi vf = 0 unknown: d= ? equation: vf 2 = vi 2 + 2 ad 0 = 242 + 2(-9. 81)d -576 = -19. 6 d 29. 4 m = d What total distance will it travel before it lands? What will be its resultant displacement when it lands? 0. m 58. 8 m

For a ball fired or thrown straight up: v=0 vi going up vf less d each second on way up 1. _______ more d each second on way down 2. ______ tdown 3. tup = _______ 2 tdown 2 tup = _____ 4. ttotal = _______ 0 5. vtop =_____ -9. 81 m/s 2 6. atop= _____ speeddown 7. speedup = ________ 8. If object falls back to its original height, then: vf=______-vi coming down

Ex. Mr. Siudy is fired directly up with an initial speed of 55 meters per second. How long will he be in the air? given: a = -9. 81 m/s 2 vi vf equation: a = Δv/t vi = 55 m/s a = (vf – vi)/t vf = -55 m/s -9. 81 = (-55 – 55)/t unknown: t = (-110)/-9. 81 t= ? t = 11 s How much time did he spend going up? t = 5. 5 s

Ex. A shot put is thrown straight down from a cliff with an initial speed of 15 m/s. How far must it fall before it reaches a speed of 35 m/s? given: a = -9. 81 m/s 2 vi = -15 m/s vf = -35 m/s unknown: d= ? equation: vf 2 = vi 2 + 2 ad (-35)2 = (-15)2 + 2(-9. 81)d 1225 - 225 = -19. 6 d 1000/(-19. 6) = d -51 m = d

2 -10 m/s C. Graphical analysis: use a ≈ _______ Ex: ball dropped from rest t (s) v (m/s) 1 3 2 t (s) d v a (m) (m/s 2) 0 0 0 -10 1 -5 -10 2 -20 -10 3 -45 -30 -10 4 -80 -40 -10 5 m -10 -20 15 m 25 m 35 m -30 -40

time total d 0 s 0 m 1 s 5 m velocity 5 m 0 m/s -10 m/s 15 m 2 s 20 m -20 m/s 25 m 3 s 45 m -30 m/s See any patterns?

Ball dropped: vectors vs. scalars displacement distance d t ~ t 2 velocity speed v t ~t d t v t acceleration a t constant a t

Ex: ball thrown straight up with vi = 30 m/s t (s) 0 d v a (m) (m/s 2) 0 30 -10 1 -10 2 -10 3 -10 4 -10 5 -10 6 -10

v (m/s) going up 30 20 25 m 10 15 m 5 m 1 2 3 4 5 -10 -20 -30 slope = _______ throughout 6 t (s)

Ex: ball thrown straight up with vi = 30 m/s t (s) d v a (m) (m/s 2) 0 0 30 -10 1 25 20 -10 2 40 10 -10 3 45 0 -10 4 -10 5 -10 6 -10

v (m/s) going up 30 coming down 20 10 25 m 15 m 5 m 1 -10 2 3 5 m 4 5 15 m 6 25 m -20 -30 slope = _______ throughout t (s)

Ex: ball thrown straight up with vi = 30 m/s t (s) d v a (m) (m/s 2) 0 0 30 -10 1 25 20 -10 2 40 10 -10 3 45 0 -10 4 40 -10 5 25 -20 -10 6 0 -30 -10

going up v (m/s) coming down positive d 30 negative d 20 10 25 m top 15 m 5 m 1 -10 2 3 5 m 4 5 15 m 6 25 m -20 -30 -10 m/s 2 slope = _______ throughout t (s)

Going down: Going up: 3 s 2 s 0 5 m 10 20 v time 0 3 s 4 s -10 15 m -20 1 s 5 s 25 m 30 -30 0 s time v 6 s

At what time is the ball at its highest point? t= 3. 0 s What are the v and a at that time? v= a = -10 m/s 2 0 How do the last 3 sec of this example compare to the example of a ball dropped from rest? the same What will the graph of speed vs. time look like? 30 20 10 1 2 3 4 5 6 t (s)

v (m/s) Ex. How does the picture change if ball is thrown up a with different initial speed, say vi = 20 m/s? 30 20 10 1 -10 -20 -30 2 3 4 5 6 t (s)

v (m/s) Ex. What if ball is thrown up with an initial speed vi = 10 m/s? 30 20 10 1 -10 -20 -30 2 3 4 5 6 t (s)

v (m/s) Ex. What if thrown down a with speed vi = 10 m/s? 30 20 10 1 2 3 4 5 6 -10 -20 -30 Ball continues down until it strikes the ground. t (s)

velocity: vf = vi + at With vi = 0 and a = -10 displacement: d = vit + ½ at 2 With vi = 0 and a = -10 vf = 0 + (-10)t d = 0 t + ½ (-10)t 2 vf = -10 t d = -5 t 2 For t = 0, 1, 2, …. vf = -10 t = -10(0) = 0 = -10(1) = -10(2) = -20 = -10(3) = -30 For t = 0, 1, 2, …. d = -5 t 2 = -5(02) = 0 = -5(12) = -5(22) = -20 = -5(32) = -45