Projectile Motion
Let’s Go Skydiving!
Speed is the distance traveled
per unit time.
Velocity is an object's speed and
direction of motion.
Acceleration is a change in
velocity over a certain period of
time.
Gravity tends to pull all objects
toward the center of the earth.
Gravitational Acceleration is the
constant describing the
acceleration of any object falling
toward the Earth.
-9.8 m/sec2
So every second something falls,
its speed increases by 9.8m/s
v = at (velocity = acceleration x time)
d = ½ a t2 (distance = ½ acceleration x
time2
v = gt (velocity = gravity x time)
d = ½ g t2 (distance = ½ gravity x time2)
0 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 0 m/sec
1 Second
Acceleration:
9.8 m/sec/sec
Velocity: 9.8 m/sec
2 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 19.6 m/sec
3 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 29.4 m/sec
4 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 39.2 m/sec
5 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 49 m/sec
6 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 58.8 m/sec
6 Seconds
Acceleration:
9.8 m/sec/sec
This is called
FREE FALL!
Velocity: 58.8 m/sec
Drop a robot from the top floor of
Williams Tower. If the robot falls for
12.2 sec. how fast will it be going when
it hits the ground?
Drop a different robot from the top floor of
the Bank of America building, which is
240 m high.
•How long does it take the robot to hit the
ground?
•How fast will it be going when it hits the
ground?
Do the problems on WRK4.1:
Free fall
A projectile is any moving object
upon which the only active force
is gravity.
Gravity pulls all projectiles toward
the center of the earth at the
same rate.
Initial Vertical Velocity (Vv) is the
upward (or downward) speed of
a projectile at the start of its flight.
Vv
Vh
Initial Horizontal Velocity (Vh) is
the forward speed of a projectile
at the start of its flight.
0 Seconds
Vv = 39.2 m
s
90 °
Acceleration:
9.8 m/sec/sec
Velocity: 39.2 m/sec
1 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 29.4 m/sec
2 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 19.6 m/sec
3 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 9.8 m/sec
4 Seconds
Acceleration:
9.8 m/sec/sec
Velocity: 0 m/sec
90°
4 Seconds
0 m/sec
3 Seconds
9.8 m/sec
2 Seconds
19.6 m/sec
1 Second
29.4 m/sec
0 Seconds
Initial Velocity (Vi)
39.2 m/sec
90°
4 Seconds
0 m/sec
5 Seconds
9.8 m/sec
6 Seconds
19.6 m/sec
7 Seconds
29.4 m/sec
8 Seconds
39.2 m/sec
4 Seconds
0 m/sec
4 Seconds
0 m/sec
3 Seconds
9.8 m/sec
5 Seconds
9.8 m/sec
2 Seconds
19.6 m/sec
6 Seconds
19.6 m/sec
1 Second
29.4 m/sec
7 Seconds
29.4 m/sec
39.2 m/sec
8 Seconds
39.2 m/sec
0 Seconds
Initial Velocity (Vi)
4 Sec.
3 Sec.
2 Sec.
1 Sec.
0 Sec.
Constant Horizontal Velocity
Constant Horizontal Velocity
4 Sec.
3 Sec.
2 Sec.
1 Sec.
0 Sec.
Gravitational Acceleration
9.8 m/sec2
Fire a bullet and drop a bullet..
• A bullet is fired perfectly horizontally, and
simultaneously, a bullet is dropped straight
down. Which one hits the ground first?
How far does he fly?
Vy= 39.2 m/s
Vx= 39.2 m/s
Vy= 39.2 m/s
Vx= 39.2 m/s
x
Another example…
• A cargo plane drops a package from an
altitude of 500m, while traveling 200 m/s.
How far does the package travel before it
hits the ground?