Projectile motion
Vectors and scalars
• A scalar quantity is described
only by its magnitude
• Examples – 5.0kg; 10.0 l;
50.0oC; 10.0m/s
Projectile motion
Vectors and scalars
• A vector quantity is described
by its magnitude and by its
direction.
• Examples – 10.0 m/s north;
2
10.0m/s down; 5.0N up.
Projectile motion
Vectors and scalars
• Vector quantities are represented by
arrows.
• The length of the arrow is proportional
to the magnitude of the vector quantity.
The head of the arrow points in the
direction of the vector. The other end
of the arrow is the tail of the vector.
Two vectors
Projectile motion
When vectors are parallel to each
other we add and subtract them in a
straightforward manner.
• If they have the same sign (point in
the same direction) we add their
magnitudes.
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.
• If they have different signs (point
in the opposite directions), we
subtract their magnitudes.
Parallel vectors – page 39
Two vectors – tail to tail
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Vectors and scalars
• We can add vectors by putting their
tails together, and drawing dotted
lines parallel to the vectors.
Two vectors with parallel lines
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Vectors and scalars
• We draw a diagonal from the point
where the two tails meet to the
opposite corner of the rectangle
that was formed.
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Vectors and scalars
• The diagonal is the sum of the two
original vectors and is called the
resultant.
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Airplane flying in crosswind (page30)
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• Frequently it is convenient to
separate vectors into perpendicular
components.
• We do this by constructing a
parallelogram that has the vector as a
diagonal.
Separating a vector into components.page 32
A velocity vector resolved into
components – page 32
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• A projectile is an object moving only
under the influence of gravity. We
also say that the object is in free fall.
• We can separate the horizontal and
vertical components of a projectile’s
velocity by using vectors.
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• The horizontal component of a
projectile’s velocity does not change.
It is constant.
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• The vertical component of a
projectile’s velocity is always changing
because it always accelerating
downward.
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• The two motions can be treated
independently.
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• Demonstration.
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• If a projectile is launched upward at
an angle, it will follow a parabolic path
if there is no air resistance.
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• In the presence of air resistance the
parabolic path is altered.
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• Satellites are projectiles that move so
fast, that the Earth curves away from
them at the same rate that they are
falling toward the earth.
• This can only happen beyond the
atmosphere where an object moving
at those speeds will not burn up fron
air friction.
Projectile motion