### angled projectiles

```Due Now:
By the end of the day
today, IWBAT…
• use trigonometry and the
kinematic equations to solve
for angled projectiles
Do Now: Calculate the magnitude of the vertical
and horizontal components of the following
vector:
65 m/s
32˚
Tuesday, November 6, 2012
Angled Projectiles
What we know about projectiles so
far…
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A projectile is any object upon which the only force is
gravity
Projectiles travel with a parabolic trajectory due to the
influence of gravity
There are no horizontal forces acting upon projectiles
and thus no horizontal acceleration
The horizontal velocity of a projectile is constant
There is a vertical acceleration caused by gravity; its
value is 9.8 m/s2, which means the vertical velocity of a
projectile changes by 9.8 m/s each second
The horizontal motion of a projectile is independent of its
vertical motion
Symmetrical Nature of a Projectile
A ball is thrown with an initial
velocity of 41.7 m/s at a 70˚ angle
Position
vx
vy
1
14.3 m/s
39.2 m/s
2
14.3 m/s
29.4 m/s
3
14.3 m/s
19.6 m/s
4
14.3 m/s
9.8 m/s
5
14.3 m/s
0
6
14.3 m/s
-9.8 m/s
7
14.3 m/s
-19.6 m/s
8
14.3 m/s
-29.4 m/s
9
14.3 m/s
-39.2 m/s
5
4
3
2
1
6
7
8
9
Horizontal vs. Angled
Horizontal Projectiles
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a of x will ALWAYS be 0
vi of y will ALWAYS be 0
a of y will ALWAYS be 9.8 m/s2
tx = ty
you must be given 3
out of 4 variables in
order to solve!
Angled Projectiles
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a of x will ALWAYS be 0
a of y will ALWAYS be 9.8 m/s2
use trig to find vi of x and
y
viy = -vfy
The vfy at the peak = 0
tx = ty
you must be given 3 out
of 4 variables in order to
solve!
Here’s a problem…

A football is kicked with an initial velocity of 25
m/s at an angle of 45-degrees with the
horizontal. Determine the time of flight of the
football.
What if…

A football is kicked with an initial velocity of 25
m/s at an angle of 45-degrees with the
horizontal. Determine the horizontal distance of
the football.
Not done yet…

A football is kicked with an initial velocity of 25
m/s at an angle of 45-degrees with the
horizontal. Determine the peak height of the
football.

A long jumper leaves the ground with an initial
velocity of 12 m/s at an angle of 28-degrees
above the horizontal. Determine the horizontal
distance AND the peak height of the long-jumper.

Li Ping Phar, the famous Chinese ski jumper,
leaves the ramp with an initial velocity of 34.9
m/s at an angle of 35°.
a. Determine the total time of flight.
b. Determine the horizontal displacement.
c. Determine the peak height (relative to the
starting height). Assume that Li lands at the
same height as the top of the ramp and that Li is
a projectile.
CHALLENEGE QUESTION!

Albert is South’s star punter for the varsity
football team. His best hang time this past
season was for a punt which he kicked at 74°
above the horizontal. The punt had a 6.2 second
hang time.
a. Determine the speed at which the ball was
punted.
b. Determine the horizontal distance which the
ball traveled.
```