P1251955650JWpMC - PowerPoint PPT Presentation

Title: P1251955650JWpMC


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Motion in Two Dimensions Galileos study of
motion included exploration of motion in two
dimensions (animations) Vectors are used to
describe motion Vectors have magnitude and
direction Scalars are simply numbers (i.e.
magnitude only) Vectors Scalars displacement di
stance velocity speed acceleration force Vecto
rs are denote by bold face or arrows The
magnitude of a vector is denoted by plain text or
vertical bars Vectors can be graphically
represented by arrows note direction and magnitude
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• Vector Addition Graphical Method of R A B
• Shift B parallel to itself until its tail is at
  the head of A, retaining its original length and
  direction.
• Draw R (the resultant) from the tail of A to the
  head of B.

the order of addition of several vectors does not
matter
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the order of addition of several vectors does not
matter
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• Vector Subtraction the negative of a vector
  points in the opposite direction, but retains its
  size (magnitude)
• A- B A ( -B)

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Resolving a Vector replacing a vector with two or
more (mutually perpendicular) vectors gt
components directions of components determined by
coordinates or geometry.
Examples horizontal and vertical North-South and
East-West
A
Ay
q
Ax
Remember basic trig SOH CAH TOA
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Example Swimming at an angle of 27º from the
horizontal, an angelfish ha a velocity v with
magnitude 25 cm/s. Find the horizontal and
vertical components of v.
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• Vector Addition by components
• R A B C
• Resolve vectors into components(Ax, Ay etc. )
• Add like components
• Ax Bx Cx Rx
• Ay By Cy Ry
• The magnitude and direction of the resultant R
  can be determined from its components.
• Strategy
• Draw a sketch and choose a coordinate system.
  Use graphical method to estimate result
• Resolve all vectors into components
• Add all x-components to get the resultant
  x-component. Add all y-components to get the
  resultant y-component.
• Determine the magnitude and direction of the
  resultant vector, as needed.

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Example Vector A has length 14 cm at 60º with
respect to the x-axis, and vector B has length
20 at 20º with respect to the x-axis. What is
the resultant of AB
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Relative Velocity Two frames of reference, one
moving relative to the other A school bus is
traveling at 20m/s relative to the crossing
guard. A boy on the bus rolls a ball from the
back of the bus to the front with a speed of 5m/s
relative to the boy. How fast does the ball go,
elative to the crossing guard? How does this
change if the ball is rolled from the front to
the back of the bus? How does this change if the
ball is rolled from the front to the back of the
bus? Relative Velocity VAC VAB VBC
velocity of A relative to C equals velocity of
A relative to B plus velocity of B relative to C
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Example A person can row a boat 5.00 km/hr in
still water tries to cross a river whose current
is 3.00 km/hr. The boat is pointed straight
across the river, but it is carried downstream by
the river as the rower rows across. What is the
velocity of the boat relative to land? How far
down stream does the boat land on the opposite
shore if the river is 200 km wide? A small
airplane with an airspeed of 200 km/hr is flown
directly north by a novice pilot from Columbia to
Charlotte. The wind is blowing from northwest to
sought east at 28 km/hr. What is the planes
resultant speed and direction relative to the
ground?
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Kinematics in Two Dimensions Rates of
change average velocity Change in vector ?
change in components! instantaneous velocity and
acceleration vectors! 3-D kinematics but
look at components...
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Example A particle is confined to move in a
horizontal plane. It starts at the origin at
t0. The particle has an initial velocity of 10
cm/s directed along the x axis and an
acceleration of 2 cm/s2 in y direction.
Compute the particles position at t1,2,3,4,5
s What is the particles velocity at
t1,3,5s? Sketch the path of the particle by
plotting the position at the indicated times.
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Projectile Motion acceleration of gravity
directed vertically down no horizontal
acceleration (taking up as y direction)
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Example A ball is thrown horizontally from the
leaning tower of Pisa with a velocity of 22 m/s.
If the ball is thrown from a height of 49 m above
the ground, where will the ball hit the ground?
discussion monkey and the dart gun
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v0
Projectile Range
q
R
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Example An arrow leaves a bow at 30 m/s. What is
its maximum range? At what two angles could the
archer point the arrow for a target 70 m away?