Examples in Chapter 3

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# Examples in Chapter 3 - PowerPoint PPT Presentation

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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### 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 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!

30 m/s

Height, H

330

150 m

Range, R

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 rock strikes ground after 4.111 s
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 It!

7.0 m

What do we know?
• arad =3 g or 10 g
• R= 7.0 m
• Need to find T
Plugging and Chugging
• arad =3 g or 10 g
• R= 7.0 m
• Need to find T
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 It

1.5 m/s

1 m/s

1.5 m/s

1 m/s

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
• 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
• 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,
• 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

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 It!

v0 m/s

8 m

600

18 m

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
• x=18 m
• y= 8 m
• a = 600
• You need to find v0
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