Kinematics and Free Fall Calculations of a Symmetrical Path Kinematical Equations Often, it is useful to relate position, velocity, and constant acceleration. The three equations for motion with constant acceleration are summarized in the table. Kinematical Equations Acceleration Due to Gravity = 9.8m/s2 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? *Because the car starts at rest, vi would be equal to 0.00 m/s. Kinematical Equations How far does the car fall? Use the equation for displacement when time and constant acceleration are known. Falling Air resistance will increase as it falls faster An upward force on the object Eventually gravity will balance with air resistance Reaches terminal velocity - highest speed reached by a falling object. Terminal velocity Force 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 Final speed 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. = Gravity is slowing the object down… -9.8 m/s2 Initial speed up Initial speed down Gravity is speeding the object up… +9.8m/s2 = Final speed down 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? Because of Symmetry… The total time = 4 s So, the time for the trip up is 2 s and the trip down is also 2 s 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?