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Examples in Chapter 3. Problem 3.23. A man stands on the roof of a 150 m tall building and throws a rock with a velocity of 30 m/s at an angle of 33 0 above the horizontal. Ignore air resistance. Calculate: The maximum height above the roof reached by the rock

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problem 3 23
Problem 3.23
  • A man stands on the roof of a 150 m tall building and throws a rock with a velocity of 30 m/s at an angle of 330 above the horizontal. Ignore air resistance. Calculate:
    • The maximum height above the roof reached by the rock
    • The magnitude of the velocity of the rock just before it strikes the ground
    • The horizontal distance from the base of the building to the point where the rock strikes the ground.
step 1 draw it
Step 1: Draw It!

30 m/s

Height, H

330

150 m

Range, R

what do we know
What do we know?
  • The x- and y-components of the initial velocity
    • Vx0=30*cos(330)=25.16 m/s
    • Vy0=30*sin(330)=16.33 m/s
  • The acceleration in the y-direction: ay=-g=-9.8
  • The acceleration in the x-direction: ax=0
  • The initial height of the rock, 150 m, = y0
  • The initial horizontal position of the rock, 0
the range of the rock
The range of the rock
  • The rock strikes ground after 4.111 s
problem 3 31
Problem 3.31

In a test of a “g-suit” a volunteer is rotated in horizontal circle of radius 7.0 m. What is the period of rotation at which the centripetal acceleration has a magnitude of

  • 3.0 g?
  • 10.0 g?
step 1 draw it10
Step 1: Draw It!

arad=3 g or 10 g

7.0 m

what do we know11
What do we know?
  • arad =3 g or 10 g
  • R= 7.0 m
  • Need to find T
plugging and chugging
Plugging and Chugging
  • arad =3 g or 10 g
  • R= 7.0 m
  • Need to find T
problem 3 37
Problem 3.37

A “moving sidewalk” in an airport moves at 1 m/s and is 35.0 m long. If a women steps on one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does she require to reach the opposite side if

  • She walks in the same direction as the sidewalk is moving?
  • She walks against the motion of the sidewalk?
step 1 draw it14
Step 1: Draw It

1.5 m/s

1 m/s

1.5 m/s

1 m/s

must find relative velocity
Must find relative velocity
  • Call the slide walk as reference frame A, therefore the woman’s velocity in this frame vA is 1.5 m/s
  • Call a stationary observer frame of reference, B and the slidewalk’s velocity in this frame is vB =1.0 m/s
  • The end points are fixed in reference B so I must adjust the woman’s velocity to reference B
two different velocities
Two different velocities
  • If the woman and slide are in the same direction:
    • Vp/B=Vp/A+VA/B
    • Vp/A= velocity of woman relative to slidewalk=1.5 m/s
    • VA/B= velocity of slidewalk relative to frame B=1.0 m/s
    • Vp/B=1+1.5=2.5 m/s
two different velocities cont d
Two different velocities cont’d
  • If the woman and slide are in the opposite directions:
    • Vp/B=Vp/A+VA/B
    • Vp/A= velocity of woman relative to slidewalk=-1.5 m/s
    • VA/B= velocity of slidewalk relative to frame B=1.0 m/s
    • Vp/B=1-1.5=-0.5 m/s
finally
Finally,
  • In the same direction: vp/B=d/t where d=35 m and Vp/B=2.5 m/s
    • t=35/2.5=14 s
  • In the opposite direction: vp/B=d/t where d=35 m and Vp/B=0.5 m/s
    • t=35/0.5=70 s
problem 3 58
Problem 3.58

A baseball thrown at an angle of 600 above the horizontal strikes a building 18 m away at a point 8 m above the point it is thrown. Ignore air resistance.

  • Find the magnitude of the initial velocity of the baseball ( the velocity with which the baseball is thrown)
  • Find the magnitude and direction of the velocity just before it strikes the building.
step 1 draw it20
Step 1: Draw It!

v0 m/s

8 m

600

18 m

the secret weapon the trajectory equation
The Secret Weapon: The Trajectory Equation
  • You can go through a lot of rigmarole but the most powerful tool in your projectile arsenal is this little formula below
you know
You know
  • x=18 m
  • y= 8 m
  • a = 600
  • You need to find v0
part b
Part B)
  • x=18 m, x0=0
  • y= 8 m, y0=0
  • a = 600
  • v0=16.55 m/s and v0x=16.55*cos(600)=8.275, voy=16.55*sin(600)=14.33
  • ax=0, ay=-9.8 m/s2
  • Need to find vx(t) and vy(t) when x=18 m