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Vertical accelerated Motion problems Quiz Tomorrow

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1 Vertical accelerated Motion problems Quiz Tomorrow
Notes: Class notes Vertical accelerated Motion problems Quiz Tomorrow Hand in elevator lab!! LATE Objectives: VDTA & PVA for vertical acceleration Understood Facts you NEED to know to work the problems Books can be turned in today

2 a: constant & (-) How to Construct a P. V. A
a: constant & (-) How to Construct a P.V.A. Diagram Position, Velocity, and Acceleration for an object moving with a constant acceleration The P.V.A. diagram: or Position are Points Velocity arrows get smaller at top Acceleration same length Acceleration and down

3 VDTA Charts for vertical motion
Going up Going down Must know !! a= -9.8 m/s/s

4 Falling objects – Need to know
Says: Dropped v i = 0m/s a = m/s/s Says: Thrown up (to maximum height) v f = 0m/s

5 First draw a line because the motion is linear
Vertical and linear Throw a ball upward with a velocity of 15 m/s. How far up does it travel in 0.5 seconds? First draw a line because the motion is linear Then make the VDTA with a chart

6 Vertical and linear Throw a ball upward with a velocity of 15 m/s
Vertical and linear Throw a ball upward with a velocity of 15 m/s. How far up does it travel in 0.5 seconds? * Decide constant velocity a = 0 or constant acceleration We know a=-9.8m/s/s so… a = constant then add dots Add the velocity arrows Going up Slowing down Add acceleration vectors

7 Vertical and linear Throw a ball upward with a velocity of 15 m/s
Vertical and linear Throw a ball upward with a velocity of 15 m/s. How far up does it travel in 0.5 seconds? * XXXX ? ?? 0.5 sec +15 m/s 0 m 0 s

8 Vertical and linear Throw a ball upward with a velocity of 15 m/s
Vertical and linear Throw a ball upward with a velocity of 15 m/s. How far up does it travel in 0.5 seconds? * XXX ? ?? 0.5 sec +15 m/s 0 m 0 s Solve the Next problem in your Notebook and wait for directions for the Whiteboard On WB Write the Equation, and answer

9 df =15m/s(.5s)+1/2(-9.8m/s/s)(0.5s)2
Vertical and linear Throw a ball upward with a velocity of 15 m/s. How far up does it travel in 0.5 seconds? df = di+ vi Δt + 1/2 a(Δt)2 * XXX ? ?? 0.5 sec +15 m/s 0 m 0 s df = di+ vi Δt + 1/2 a(Δt)2 df =15m/s(.5s)+1/2(-9.8m/s/s)(0.5s)2 df =7.5m m df =6.3 m

10 wait for directions for the Whiteboard “VDTA” Chart with numbers
A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo. * Solve the Next problem in your Notebook and wait for directions for the Whiteboard On WB; Write the “VDTA” Chart with numbers Equation, and Answer with Label

11 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(2.62m)
A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo. 0 m/s 2.62 m XXX ?? 0 m 0 s * Maximum Height!! vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(2.62m) 0 = vi (m/s)2 51.352(m/s)2 = vi2 7.16 m/s = vi

12 Throw down from height of 5.6 m with 1.4 m/s Vf is?
(-) velocity goes here

13 Throw down from height of 5.6 m with 1.4 m/s Vf is?
-1.4 m/sec * vf2 = vi2 + 2a (df - di) 5.6 m vf2 =(-1.4)2+ 2(-9.8m/s/s)(-5.6m) 0 sec vf2 = vf2 = ??? vf = +/ m/s 0 m XXXXX vf = m/s

14 Whiteboards and Markers ready
Vertical freefall quiz Whiteboards and Markers ready Test tomorrow: VDTA and PVA Problems Horizontal and vertical Including freefall Vertical problems

15 Math part of Test tomorrow on:
Be able to do the following: Horizontal VDTA and PVA problems (a=0 or a≠0) Vertical VDTA and PVA problems (a=0 or a≠0) Vertical FBD problems (For accel. a=0 or a≠0) Vertical FBD problems (Freefall  a = -9.8m/s/s) Concept part of Test tomorrow on: Know the following terms and concepts: Velocity, Displacement, Acceleration, Vector, Scalar, Magnitude, Direction Freefall, Terminal velocity, Air Resistance Net force, Balanced Force, Unbalanced Forces When Acceleration + or – Acceleration from FBD problem to VDTA Know the elevator pattern: net Force & acceleration Questions about skydiving

16 vf2 = vi2 + 2a (df - di) vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m)
VDTA and PVA going DOWN A 25 gram walnut is dropped from a height of 6.5 meters. What speed does it hit the ground? vf2 = vi2 + 2a (df - di) 6.5 vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m) vf2 = vf2 = m2/s2 ? X Take square root vf = +/ m/s Decide + or - vf = m/s

17 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m)
VDTA and PVA going UP A baseball is thrown straight up. It get to a maximum height of 4.5 meters. What was the initial velocity? vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m) 4.5 0 = vi (m/s)2 XX +88.2(m/s)2 = vi2 Take square root ?? +/ m/s = vi Decide + or - vf = m/s

18 Math part of Test tomorrow on:
Be able to do the following: Horizontal VDTA and PVA problems (a=0 or a≠0) Vertical VDTA and PVA problems (a=0 or a≠0) Vertical FBD problems (For accel. a=0 or a≠0) Vertical FBD problems (Freefall  a = -9.8m/s/s) Concept part of Test tomorrow on: Know the following terms and concepts: Velocity, Displacement, Acceleration, Vector, Scalar, Magnitude, Direction Freefall, Terminal velocity, Air Resistance Net force, Balanced Force, Unbalanced Forces When Acceleration + or – Acceleration from FBD problem to VDTA Know the elevator pattern: net Force & acceleration Questions about skydiving

19 vf = vi + a (tf - ti) vf =(0)2+ (-9.8m/s/s) (tf - 0)
A penny is dropped from the top of a tall building. It takes 12.8 seconds to hit the ground. How fast is the penny going in m/s just before it hits the ground? How tall is the building? vf = vi + a (tf - ti) 6.5 vf =(0)2+ (-9.8m/s/s) (tf - 0) vf2 = (12.8) vf2 = 125.m2/s2 ? 12.8 Take square root tf = s

20 vf = vi + a (tf - ti) vf =(0)2+ (-9.8m/s/s) (tf - 0)
A penny is dropped from the top of a tall building. It takes 12.8 seconds to hit the ground. How fast is the penny going in m/s just before it hits the ground? How tall is the building? vf = vi + a (tf - ti) 6.5 vf =(0)2+ (-9.8m/s/s) (tf - 0) vf = (12.8) vf = m/s ? 12.8

21 vf = vi + a (tf - ti) vf =(0)2+ (-9.8m/s/s) (tf - 0)
A penny is dropped from the top of a tall building. It takes 12.8 seconds to hit the ground. How fast is the penny going in m/s just before it hits the ground? How tall is the building? How long did it take? vf = vi + a (tf - ti) 6.5 vf =(0)2+ (-9.8m/s/s) (tf - 0) vf2 = (12.8) vf2 = 125.m2/s2 ? 12.8 Take square root tf = s

22 vf 2= vi2 + 2a (df - di) -125. =(0)2+ 2(-9.8m/s/s) (df - di)
A penny is dropped from the top of a tall building. It takes 12.8 seconds to hit the ground. How fast is the penny going in m/s just before it hits the ground? How tall is the building? vf 2= vi2 + 2a (df - di) ?? -125. =(0)2+ 2(-9.8m/s/s) (df - di) 15625= 0 + (-19.8m/s/s) (0- di) 15625= (-19.8m/s/s) (0- di) xx 12.8 di = 797 m

23 vf2 = vi2 + 2a (df - di) 0 = (9.6)2 + 2(-9.8m/s/s)(df)
A rock is thrown to the top of a flag pole with an initial upward velocity of 9.6 m/s. The rock’s peak is at the top of the pole. How far above the point of release is the flagpole's top? vf2 = vi2 + 2a (df - di) 0 = (9.6)2 + 2(-9.8m/s/s)(df) ?? 0 = (df) XX / -19.6= df 4.7 m = df 9.6

24 vf2 = vi2 + 2a (df - di) vf2 =(0)2 + 2(-9.8m/s/s)(-12.5m)
A penny is dropped from the top of a 12.5 meter tall building. How fast is the penny going in m/s just before it hits the ground? How long is the penny in the air? vf2 = vi2 + 2a (df - di) 12.5 vf2 =(0)2 + 2(-9.8m/s/s)(-12.5m) vf2 = m2/s2 vf2 = m2/s2 ? X Take square root vf = +/ m/s Decide + or - vf = m/s

25 vf = vi + a (tf - ti) vf =(0) + (-9.8m/s/s)(tf - 0)
A penny is dropped from the top of a 12.5 meter tall building. How fast is the penny going in m/s just before it hits the ground? How long is the penny in the air? vf = vi + a (tf - ti) 12.5 vf =(0) + (-9.8m/s/s)(tf - 0) -49.5 m/s = tf tf = s ? X

26 Rest of slides are work in progress

27 vf2 = vi2 + 2a (df - di) vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m)
. If you throw a ball downward with an initial speed of 15 m/sec, what is the time it takes to hit the ground if it starts 3.7 meters up from the ground? What is the velocity just before it hits the ground? vf2 = vi2 + 2a (df - di) 6.5 vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m) vf2 = vf2 = m2/s2 ? X Take square root vf = +/ m/s Decide + or - vf = m/s

28 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m)
A student throws a ball up at a speed of 5.6 m/s. What is the highest it goes up? vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m) 4.5 0 = vi (m/s)2 XX +88.2(m/s)2 = vi2 Take square root ?? +/ m/s = vi Decide + or - vf = m/s

29 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m)
If you throw a ball upward with an initial speed of 15 m/sec, what is the height of the ball at its peak? vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m) 4.5 0 = vi (m/s)2 XX +88.2(m/s)2 = vi2 Take square root ?? +/ m/s = vi Decide + or - vf = m/s

30 vf2 = vi2 + 2a (df - di) vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m)
A student drops a ball from the top of a tall building and it takes 2.8 s to reach the ground. (a) What was its velocity just before hitting the ground? (b) Find the height of the building. vf2 = vi2 + 2a (df - di) 6.5 vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m) vf2 = vf2 = m2/s2 ? X Take square root vf = +/ m/s Decide + or - vf = m/s

31 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m)
A student throws a ball up at a speed of 3.6 m/s. What is the highest it goes up? How long does it take to get to the maximum height? vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m) 4.5 0 = vi (m/s)2 XX +88.2(m/s)2 = vi2 Take square root ?? +/ m/s = vi Decide + or - vf = m/s

32 vf2 = vi2 + 2a (df - di) vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m)
. If you throw a ball downward with an initial speed of 15 m/sec, what is the time it takes to hit the ground if it starts 7.3 meters up from the ground? What is the velocity just before it hits the ground? vf2 = vi2 + 2a (df - di) 6.5 vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m) vf2 = vf2 = m2/s2 ? X Take square root vf = +/ m/s Decide + or - vf = m/s

33 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m)
A rock is thrown to the top of a flag pole with an initial upward velocity of 19.6 m/s. The rock’s peak is at the top of the pole. How far above the point of release is the flagpole's top? vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m) 4.5 0 = vi (m/s)2 XX +88.2(m/s)2 = vi2 Take square root ?? +/ m/s = vi Decide + or - vf = m/s

34 vf2 = vi2 + 2a (df - di) vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m)
A penny is dropped from the top of a tall building. It takes 5.5 seconds to hit the ground. How fast is the penny going in m/s just before it hits the ground. How tall is the building? vf2 = vi2 + 2a (df - di) 6.5 vf2 =(0)2 + 2(-9.8m/s/s)(-6.5m) vf2 = vf2 = m2/s2 ? X Take square root vf = +/ m/s Decide + or - vf = m/s

35 vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m)
A rock is thrown to the top of a flag pole with an initial upward velocity of 8.5 m/s. The rock’s peak is at the top of the pole. How far above the point of release is the flagpole's top? vf2 = vi2 + 2a (df - di) 0 = vi2 + 2(-9.8m/s/s)(4.5m) 4.5 0 = vi (m/s)2 XX +88.2(m/s)2 = vi2 Take square root ?? +/ m/s = vi Decide + or - vf = m/s

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