Projectile motion - Mr. Miller's Class
Transcript of Projectile motion - Mr. Miller's Class
Projectile Examples
• Tennis ball
• Golf ball
• Football
• Softball
• Soccer ball
• Bullet
• Hockey puck
• Basketball
• Volleyball
• Arrow
• Shot put
• Javelin
These are all examples of things that are
projected, then go off under the
influence of gravity
The key to understanding
projectile motion is to realize
that gravity acts vertically
it affects only the vertical
part of the motion, not the
horizontal part of the motion
Understanding Projectiles
Demonstration
• We can see that the horizontal and vertical motions are independent
• The red ball falls vertically
• The yellow ball was given a kick to the right.
• They track each other vertically step for step and hit the ground at the same time
In the absence of gravity a bullet
would follow a straight line forever.
With gravity it FALLS AWAY from
that straight line!
Projectile Paths
Sample Problem
A zookeeper finds an escaped monkey hanging from a light pole. Aiming her tranquilizer gun at the monkey, she kneels 10.0 m from the light pole,which is 5.00 m high.
The tip of her gun is 1.00 m above the ground. At the same moment that the monkey drops a banana, the zookeeper shoots.
If the dart travels at 50.0 m/s,will the dart hit the monkey, the banana, or neither one?
1 . Select a coordinate system.
The positive y-axis points up, and the positive x-axis points along the ground toward the pole. Because the dart leaves the gun at a height of 1.00 m, the vertical distance is 4.00 m.
Sample Problem
2 . Use the inverse tangent function to find the angle that the initial velocity makes with the x-axis.
1 1 4.00 mtan tan 21.8
10.0 m
y
x
Sample Problem
3 . Choose a kinematic equation to solve for time.
Rearrange the equation for motion along the x-axis to isolate the unknown t, which is the time the dart takes to travel the horizontal distance.
x (vi cos )t
t x
vi cos
10.0 m
(50.0 m/s)(cos 21.8) 0.215 s
Sample Problem
4 . Find out how far each object will fall during this time. Use the free-fall kinematic equation in both cases.
For the banana, vi = 0. Thus:
yb = ½ay(t)2 = ½(–9.81 m/s2)(0.215 s)2 = –0.227 m
Sample Problem
The dart has an initial vertical component of velocity equal to vi sin , so:
yd = (vi sin )(t) + ½ay(t)2
yd = (50.0 m/s)(sin 21.8)(0.215 s) +½(–9.81 m/s2)(0.215 s)2
yd = 3.99 m – 0.227 m = 3.76 m
Sample Problem
5 . Analyze the results.
Find the final height of both the banana and the dart.
ybanana, f = yb,i+ yb = 5.00 m + (–0.227 m)
ybanana, f = 4.77 m above the ground
Sample Problem
The dart hits the banana.
The slight difference is due to rounding.
ydart, f = yd,i+ yd = 1.00 m + 3.76 m
ydart, f = 4.76 m above the ground
Sample Problem
Newton’s First Law of Motion
• “Every object continues in its state of rest, or
of uniform motion in a straight line, unless it is
compelled to change that state of motion by
forces impressed upon it ”
• The tendency of matter to maintain its state
of motion is known as INERTIA.
Path of the Projectile
v
Distance downfield
(range)
Heig
ht rising falling
projectile
g
Horizontal velocity
Vertical
velocity
v
Vertical Motion
210 0 2
210 0 0 2
0
0 0
(2 15)
sin (4 22)
(2 11)
sin (4 23)
y y
y y y
y
y y v t a t
y y v t gt
v v a t
v v gt
Projectile motion – key points
1) The projectile has both a vertical and horizontal component of velocity
2) The only force acting on the projectile once it is shot is gravity (neglecting air resistance)
3) At all times the acceleration of the projectile is g = 9.8 m/s2 downward
4) The horizontal velocity of the projectile does not change throughout the path
Key points, continued
5) On the rising portion of the path gravity
causes the vertical component of velocity to
get smaller and smaller
6) At the very top of the path the vertical
component of velocity is ZERO
7) On the falling portion of the path the vertical
velocity increases
More key points
8) If the projectile lands at the same elevation as its starting point it will have the same vertical SPEED as it began with
9) The time it takes to get to the top of its path is the same as the time to get from the top back to the ground.
10) The range of the projectile (where it lands) depends on its initial speed and angle of elevation
A 2.00 m tall basketball player wants to make a basket from
a distance of 10.0 m. If he shoots the ball at a 450 angle, at
what initial speed must he throw the ball so that it goes
through the hoop without striking the backboard?
y
x y0
Sample Problem
210 0 2
210 0 0 2
0
0 0
(2 15)
sin (4 22)
(2 11)
sin (4 23)
y y
y y y
y
y y v t a t
y y v t gt
v v a t
v v gt
210 0 2
0 0 0cos
x xx x v t a t
x x v t
0
0 0
0
cos
x x x
x
x
v v a t
a
v v
Equations to Choose from
Maximum Range
• When an artillery shell is fired the initial speed of the projectile depends on the explosive charge – this cannot be changed
• The only control you have is over the angle of elevation.
• You can control the range (where it lands) by changing the angle of elevation
• To get maximum range set the angle to 45°
Interactive
• http://galileo.phys.virginia.edu/classes/109N/
more_stuff/Applets/ProjectileMotion/jarapplet
.html
• http://jersey.uoregon.edu/vlab/Cannon/