Transcript Vertical motion of a projectile Δy =

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.
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!!
By deriving new formulas,
We get the following…
Vertical motion of a projectile
Δy = - ½g(Δt)2
Vyf = -gΔt
Vyf2 = -2gΔy
Horizontal motion of a projectile
Δx = vxΔt
vx = vxi = constant
R = v02 sinθ
g
But what if an object is launched
At an angle…
Δx = vi (cos θ)Δt
vx = vi (cos θ) = constant
Δy = vi (sin θ)Δt – ½g(Δt)2
vxf = vi(sin θ) - gΔt
vyf2 = vi2(sin θ)2 – 2gΔy
Certain angles will travel
Distances that are equal to
Other angles.
75° = 15°
60° = 30°
45° travels the farthest
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
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
The centripetal force is the
Necessary net force exerted in
The centripetal direction to
Cause circular motion.
2r
4π
ac = 2
T
4π2r
Fc = m
T2
T = the period,
The time needed
To one complete
revolution
v
r
a
v
r
v
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
A frame of reference is a
Coordinate system for specifying
The precise location of objects
In space.
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.
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