Post on 26-Mar-2015
transcript
Kinematics in 2-D
Review - What is Kinematics???
• Describes the motion of objects• Uses a set of equations• Draws a relationship between time, distance,
velocity, and acceleration
We Started in 1-D
• One dimensional motion (1-D)– Motion only in one plane (either in the x-direction
or the y-direction)– Motion in a straight line
Now Let’s Do it in 2-D
• Two Dimensional Motion– Instead of motion in either the x-direction or the
y-direction, we have motion in both the x-direction and the y-direction
– The motion is no longer in a straight line; it is parabolic
The Projectile
• Any object that travels through the air in which the only force acting on it is gravity
What are some example of projectiles?
And another…
Some Important Things to Know
• Projectiles travel in 2 dimensions, in the x-direction AND in the y-direction
• The ONLY force acting on a projectile is gravity• The motion in the x-direction is COMPLETELY
INDEPENDENT of the motion in the y-direction…let’s take a look
One More Look at Some Projectiles
Sign Conventions
• Positive directions (+d)– Right– Up
• Negative directions (-d)– Left– Down
• Now it is important as ever!!!
The Good News…
• The same equations from 1-D kinematics apply in 2-D
vtd
atvv if
2
2
1attvd i
advv if 222
Solving Problems
1. Draw a picture of the problem2. Define your sign convention
1. It is your decision, but use one that is convenient2. Typically, up is positive and right is positive
3. Separate the x-components and the y-components so you can solve them separately
4. Use the GUESS method
Remember g?
• Earlier, we said g for the surface of the Earth equals 9.81 m/s2
• We were not taking into consideration the direction in which g works
• What do you think g is?
2/81.9 smg
Crazy Important…
• The motion in the x-direction is COMPLETELY INDEPENDENT of the motion in the y-direction
• There is one link between the x-direction and the y-direction, and it is
t
Lingo and Such
Terms• Projectile• Trajectory• Range• Altitude• Hang time
Variables/Constants
• Vi,x or V0,x
• Vi,y or V0,y
• Vf,x
• Vf,y
• t• d or h• g
Example Problem
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
• Step 1: Draw a Picture
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
• Step 1: Draw a Picture• Step 2: Define a Sign
Convention
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
• Step 1: Draw a Picture• Step 2: Define a Sign
Convention• Step 3: Pick the
direction you want to start in and solve!
Let’s Start in the Y Direction
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
Given:d = -1050 mg = -9.8 m/s2
Unknown:t = ?
Equation:
2
2
1gtd
Let’s Start in the Y Direction
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
Substitute:
Solve:
2)8.9(2
11050 t
sec6.14t
2
2
1gtd
sec6.14t
Now Let’s Solve the X-Direction
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
Given:vi,x = +115 m/s
t = 14.6 secUnknown:
dx = ?
Equation:
vtd
Now Let’s Solve the X-Direction
An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?
Substitute:
Solve:
vtd
md 1679
)6.14)(115(d
1679 meters
Practice #1
A car drives off a cliff that is 50 m high. When it lands, investigators measure that the car is 85 m away from the base of the cliff. Calculate the following:
(1)the time the car was in the air.(2)the horizontal velocity of the car when it
drove off the cliff?
Practice #2
You throw a ball straight up with an initial vertical velocity of 22 m/s. Calculate the following:
(1)the time the ball is in the air.(2)how high the ball goes.