### 1) quickly lag behind the plane while falling 2) remain vertically

```UNIT 2
Two Dimensional Motion
And Vectors
1
ConcepTest 3.5
You drop a package from
a plane flying at constant
speed in a straight line.
Dropping a Package
1) quickly lag behind the plane
while falling
2) remain vertically under the
plane while falling
Without air resistance, the
3) move ahead of the plane while
falling
package will:
4) not fall at all
2
ConcepTest 3.5
You drop a package from
a plane flying at constant
speed in a straight line.
Dropping a Package
1) quickly lag behind the plane
while falling
2) remain vertically under the
plane while falling
Without air resistance, the
3) move ahead of the plane while
falling
package will:
4) not fall at all
Both the plane and the package have
the same horizontal velocity at the
moment of release. They will maintain
this velocity in the x-direction, so they
stay aligned.
Follow-up: What would happen if air resistance is present?
3
ConcepTest 3.6b
Dropping the Ball II
1) the “dropped” ball
In the previous problem,
2) the “fired” ball
which ball has the greater
3) neither – they both have the
same velocity on impact
velocity at ground level?
4) it depends on how hard the
ball was thrown
4
ConcepTest 3.6b
Dropping the Ball II
1) the “dropped” ball
In the previous problem,
2) the “fired” ball
which ball has the greater
3) neither – they both have the
same velocity on impact
velocity at ground level?
4) it depends on how hard the
ball was thrown
Both balls have the same vertical velocity
when they hit the ground (since they are
both acted on by gravity for the same
time). However, the “fired” ball also has a
horizontal velocity. When you add the two
components vectorially, the “fired” ball
has a larger net velocity when it hits the
ground.
Follow-up: What would you have to do to have them
both reach the same final velocity at ground level?
5
Monday September 26
Projectiles: Launch At Any Angle
6
TODAY’S AGENDA
Monday, September 26
 Projectile Motion
 Mini-Lesson: Launch At Any Angle
 Hw: Complete Practice D Problems (all)
UPCOMING…
Tues: LAB 3: Projectile Motion
Wed: More Projectile Motion
Thurs: Problems @ the Boards
Fri:
Problem Quiz 2 Projectile Motion
 Mon: Problems @ the Boards
 Tues: CH 3 TEST




7
Demonstration with MythBusters
Demonstration with Dr. Walter Lewin
8
General Launch Angle
9
General Launch Angle
10
Resolving the Velocity
11
Resolving the Velocity
12
Projectile Motion Equations
Horizontal
Velocity
Eq 1
Vertical
Velocity
Eq 2
Eq 3
Horizontal
Displacement
Eq 4
13
Projectile Motion Equations
Vertical
Displacement
Eq 5
Range
Eq 6
Time to
the Top
Eq 7
14
Sample Problem
A golfer hits a golf ball at an angle of 25.0˚ to the
ground. If the golf ball covers a horizontal distance of
301.5 m, what is the ball’s maximum height?
(Hint: At the top of its flight, the ball’s vertical velocity
component will be zero.)
Consider the Range equation:
Solve for the
Now find time to the top:
15
Find the vertical height at 2.68 s:
16
Sample Problem
A potato is shot from a potato gun at 100.0 m/s at an
angle of 45.0˚. The potato is shot from a bridge 50.0 m
above the water. Find the following:
a)
b)
c)
d)
total time of flight
final velocity just before hitting the water
total horizontal displacement
maximum vertical displacement above the water
17
What must I do first?
Break the initial velocity into
x- and y- components.
Which question is easiest to answer?
Find the total time of flight
Which equation has all the information but time?
By quadratic equation, t = 15 s
18
Without the quadratic formula solve for t:
2 STEPS:
i. Find final velocity in y-axis
ii. Find time
19
What is the final velocity?
20
What is the total horizontal displacement?
What is the maximum vertical displacement above the water?
21
Sample Problem
.82 s
22
END
23
```