Kinematics and Free Fall

Calculations of a Symmetrical Path

Kinematical EquationsOften, it is useful to relate position, velocity, and constant acceleration.

The three equations for motion with constant acceleration are summarized in the table.

Suppose the free-fall ride at an amusement park starts at rest and is in free fall for 1.5 s. What would be its velocity at the end of 1.5 s?

Kinematical Equations

Acceleration Due to Gravity = 9.8m/s2

*Because the car starts at rest, vi would be equal to 0.00 m/s.

How far does the car fall?

Kinematical Equations

Use the equation for displacement when time and constant acceleration are known.

Falling

Air resistance will increase as it falls fasterAn upward force on the objectEventually gravity will balance with air resistanceReaches terminal velocity - highest speed reached by a falling object.

Terminal velocityForce of gravity is constant

air resistance increases as you speed up until the force is equal

Equal forces, no acceleration constant velocity at terminal velocity

THROWING OBJECTS UP

We talked about what happens when an object is thrown into the air…

• It slows down as it go up.

• At the highest point, it stops.

• As it falls, it speeds up… We have done the falling objects.

Initial speed up Final speed down=

Initial speed downFinal speed up =

Gravity is slowing the object down… -9.8 m/s2

Gravity is speeding the object up… +9.8m/s2

Going up!When throwing an object into the air, an initial speed must be given to the object.If the object is a stomp rocket, then the AIR is what gives the rocket its initial speed.At the top of the flight… the highest point… the speed is 0.Gravity is slowing the object down with an acceleration of – 9.8 m/s2.

Going Down!

This is what we have done before.

When dropping something, initial speed is 0.

An object falls because of gravity with an acceleration of 9.8 m/s2.

Symmetry

What goes up must come down… and in a symmetrical pattern.

What is symmetry?A regular arrangement,

corresponding in size, form, and arrangement

of parts on opposite sides of a line

• In other words, both sides are even

• The up side looks exactly like the down side, except for direction.

Because of Symmetry…

Since the initial speed up is the same as the final speed down…Since the initial speed down is the same as the final speed up…Since gravity is 9.8 m/s2, even though one is positive and one is negative…Since the object travels the same distance up as it does down…

Because of Symmetry…

It stands to reason that the time it takes for the object to travel up EQUALS

The time it takes for the object to travel down.

If you want the object to go higher, what must you do? How does that change the total time for the trip?

The total time = 4 s

So, the time for the trip up is 2 s and the trip down is also 2 s

Because of Symmetry…

What does that mean for your stomp rockets?

Look at the data table.

Calculate how high the highest stomp rocket went?

What is the main reason one rocket goes higher than another?