9 motion in a plane
TRANSCRIPT
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MOTION IN A PLANE
PROJECTILE MOTION
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Motion in a Plane
refers to the motion of an
object traversing a curved
path which lies in a fixed
plane
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Projectile Motion
a motion in which an
object is given an initial
velocity and which is then
allowed to move under the
action of its weight (or
gravity) alone
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ex. bullet shot from a gun
bomb released from an
aircraft
a ball thrown horizontally
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Projectile motion is a combination
of:
1. constant horizontal velocity
vxo = vx = constant
ax = constant = 0
2. uniformly accelerated vertical
motion
ay = constant = g
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Range, R
the horizontal distance from
the starting point to the point
at which the projectile return to
its original level
maximum horizontal
displacement
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Time of Flight, T
the time that elapses from
the instant the projectile is
released until it hits the
ground
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Equations for Projectile
Motion
are based on equations for
uniformly accelerated motion
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a. An object which is given an
initial horizontal velocity, vxi
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b. An object which is given an
initial velocity, vi at a
certain angle θ with the
horizontal
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Exercises
1. A stone is thrown with a
velocity of 35 m/s in a
horizontal direction from the
top of a tall building. Find its
velocity and displacement
after 2 seconds.
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2. A ball is thrown horizontally
with a velocity of 40 m/s
from a window 44.1 m from
the ground. Find the time of
flight and the range.
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3. A stone is thrown horizontally
from a building 122.5m high. If
the stone travels 25 m before
striking the ground, after how
many seconds will it reach the
ground? What is its initial
velocity?
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4. A ball is thrown at 38.7o
above the horizontal with a
speed of 32 m/s. Find:
a. the horizontal and vertical
components of the initial
velocity.
b. the magnitude of velocity
after 3 seconds
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c. the time required to return
to its original level
d. maximum height reached
e. the range
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SW ½ cross.
1. A bullet has a speed of
2000 ft/s as it leaves a rifle.
If it is fired horizontally from
a cliff 24 ft above a lake, find
the range and time of flight
of the bullet.
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2. Jude threw a ball horizontally
at a speed of 12 m/s, from a
third floor building, 20 m high.
Ignoring air resistance, how
long will it take for the ball to
reach the ground? How far from
the building will it strike?
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3. A projectile is fired at an angle
of 30o with the horizontal with a
speed of 600 m/s. Find the
horizontal and vertical
components of the initial
velocity. What is the maximum
height, range, and time of
flight?