Transcript Projectile Motion or Two Dimensional Kinematics

Projectile Motion or
Two Dimensional Kinematics
SP1. Students will analyze the relationships between
force, mass, gravity, and the motion of objects.
b. Compare and contrast scalar and vector quantities.
f. Measure and calculate two-dimensional motion (projectile) by
using component vectors.
What is a projectile?
 A projectile is any object that is cast, fired,
flung, heaved, hurled, pitched, tossed, or thrown.
(This is an informal definition.)
 The path of a projectile is called its trajectory.
 When a projectile moves horizontally
with constant velocity while being
accelerated vertically, the result is
parabolic motion.
How is projectile motion 2-D?
 Projectile motion is a combination of
horizontal motion and vertical motion.
 The horizontal motion of a projectile is
constant because no gravitational force
acts horizontally.
 The vertical motion of a projectile is
nothing more than free fall with a
constant downward acceleration due to
gravity.
Horizontal Launch
Vertical Launch
Does launch velocity matter?
Does launch velocity matter?
Projectile Simulator
Check Your Understanding
Suppose a snowmobile is equipped with a
flare launcher which is capable of launching
a sphere vertically.
If the snowmobile is in motion, launches the
flare, and maintains a constant horizontal
velocity after the launch, where will the flare
land (neglect air resistance)?
Check Your Understanding
Suppose an airplane drops a flare while it
is moving at constant horizontal speed at
an elevated height.
Assuming that air resistance is negligible,
where will the flare land relative to the
plane?
A. Directly below the plane.
B. Below the plane and ahead of it.
C. Below plane and behind it.
Why does the horizontal component of a
projectile’s motion remain constant?
Because no force acts on it horizontally.
Why does the vertical component of a
projectile’s motion undergo change?
Because gravity is pulling it downward.
How does the vertical distance a projectile
falls below an otherwise straight-line path
compare with the vertical distance it would
fall from rest in the same time?
The vertical and horizontal distances
are equal.
A projectile is launched vertically at 100
m/s. If air resistance can be neglected, at
what speed does it return to its initial
level?
100 m/s
Solving projectile problems…
 Horizontal (x) Component
 Since there is NO acceleration in the x-direction, any
equation with a cannot be used, leaving us with
vx = Δx / t
Solving projectile problems…
 Vertical (y) Component
 Since there IS acceleration in the y-direction, any
equation with a (really g) can be used…
vfy = viy + gt
Δy = viyt + ½ gt2
vfy2 = viy2 + 2gΔy
Ex 1: A student sits on the roof of her house which is
12 m high. She can launch water balloons from a
slingshot at 25 m/s. If she fires a water balloon
directly horizontally:
a. How long will it be airborne?
b. How far will it travel?
c. How fast is the balloon falling vertically?
Ex 2: A bullet traveling 800 m/s horizontally hits a
target 180 m away.
a. How fast is the bullet falling vertically?
b. How far does the bullet fall before it hits the target?
c. How long does it take to hit the target?
Ex 3: A ball is thrown horizontally from the roof of a
building 50 m tall and lands 45 m from the base.
a. How long does it take to hit the ground?
b. How fast is the ball falling vertically?
c. What was the ball’s initial speed?
Ex 4: A person kicks a rock off a cliff horizontally with a
speed of 20 m/s.
It takes 7.0 seconds to hit the ground.
a. What is the height of the cliff?
b. What is the final vertical velocity?
c. What is the range of the projectile?
Ex 5: A golfer practicing on a range with an elevated tee
4.9 m above the fairway is able to strike a ball with a
horizontal velocity of 20 m/s.
a. How long will the ball take to land?
b. How far will the ball travel before landing?
c. What is the acceleration of the ball 0.5 s after being
hit?
d. Calculate the speed of the ball 0.80 s after it leaves the
club.
e. With what speed will the ball hit the ground?