Motion

The symbol “Δ” means “Change in”

Quantity Symbol Definition Units Quantity Symbol Definition Unit

Distance d m Displacement d m

Speed v d/Δt m/s Velocity v d/Δt m/s

Acceleration a Δv/Δt m/s2 Acceleration a Δv/Δt m/s2

x

y

Motion

Air Hockey

There is no friction between the puck and the table surface

a = 0

Motion

Free Fall Tower

Drop distance - dd

y Height above base - y

100 m

Assumption: No air resistance

Motion

Air Hockey, Free Fall Tower Revisited

d

y

100 m

Assumption: No air resistanceAssumption: No friction

2D Motion

Path Characteristics

2D Motion

Path Characteristics

* The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions

2D Motion

Path Characteristics

* The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions

* What happens in the vertical direction is independent of what happens in the horizontal direction

2D Motion

Path Characteristics

* The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions

* What happens in the vertical direction is independent of what happens in the horizontal direction

* The actual path is mathematically that of a parabola. The path of any projectile in free fall will be that of a parabola

2D Motion

Path Characteristics

* The combined graph of the two independent motions is identical to the actual motion of an object in free fall (projectile) in two dimensions

* What happens in the vertical direction is independent of what happens in the horizontal direction

* The actual path is mathematically that of a parabola. The path of any projectile in free fall will be that of a parabola

* In General:

Vertical drop distance is given by d = ½ a t2

Horizontal distance is given by x = vt

2D Motion

A cannon and a rifle is held so that their barrels are horizontal and the same height above the ground. A marble is held at the same height above the ground. At exactly the same time, the cannon an rifle are fired and the marble is dropped. Which one hits the ground first?

A locomotive has a vertical smoke stack. The train moves at a constant velocity. A projectile is fired out of the stack (in a vertical direction). Will the projectile land in front of the train, behind the train, or back in the stack?

2D Motion

A person stands at the edge of a cliff which is 5 m high. The person throws a ball (m = 2 kg) horizontally with a speed of 2 m/sec. How far from the base of the cliff does the ball land?

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