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Motion in 2 Dimensions

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Neglecting air resistance, They will hit the ground at the. Same ... Certain angles will travel. Distances that are equal to. Other angles. 75 = 15 60 = 30 ... – PowerPoint PPT presentation

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Title: Motion in 2 Dimensions


1
Chapter 6 Motion in 2 Dimensions
2
6.1 Projectile Motion
Projectile Motion is the motion Of objects
moving In two Dimensions under the influence Of
gravity.
Projectiles follow parabolic paths This path is
called the trajectory.
3
Projectile motion is free fall With an initial
horizontal velocity.
If a ball is dropped, and another Ball is
launched horizontally, Neglecting air
resistance, They will hit the ground at the Same
time!!
4
By deriving new formulas, We get the following
Vertical motion of a projectile
?y - ½g(?t)2
Vyf -g?t
Vyf2 -2g?y
5
Horizontal motion of a projectile
?x vx?t
vx vxi constant
R v02 sin?
g
6
But what if an object is launched At an angle
?x vi (cos ?)?t
vx vi (cos ?) constant
?y vi (sin ?)?t ½g(?t)2
vxf vi(sin ?) - g?t
vyf2 vi2(sin ?)2 2g?y
7
Certain angles will travel Distances that are
equal to Other angles.
75 15 60 30 45 travels the farthest
8
PROBLEM...
A ball is launched with an initial Velocity of
4.5 m/s at an angle Of 66 above the horizontal.
What Was the maximum height of The ball? How
long did it take For the ball to hit the ground?
y 0.86m t 0.84s
9
6.2 Circular Motion
Uniform Circular Motion is Motion at constant
speed around A circle with a fixed radius.
Centripetal Acceleration is the Center directed
acceleration of An object in uniform circular
motion
10
The centripetal force is the Necessary net force
exerted in The centripetal direction to Cause
circular motion.
4p2r T2
ac
4p2r T2
Fc m
11
T the period, The time needed To one
complete revolution
v
r
r
v
a
v
12
PROBLEM...
A 13g rubber stopper is attached To a 0.93 m
string. The stopper is Swung in a horizontal
circle, Making one revolution in 1.18s. Find
the tension force exerted By the string on the
stopper.
0.34 N
13
6.3 Relative Velocity
A frame of reference is a Coordinate system for
specifying The precise location of objects In
space.
14
Velocity measurements differ In different frames
of reference.
For example, if you bounce a ball In an elevator,
the ball will fall at g relative to the ground,
but Its acceleration will be faster To the
elevator when going up.
15
PROBLEM...
A Boat traveling east at a speed Of 4 m/s. John
rolls a marble With a velocity of 0.75 m/s
north, Straight across the deck. What Is the
velocity of the marble Relative to the water?
4.1 m/s at 11 north of east
16
THE END
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