What’s the hurry? The Kinematics of Freefall

Falling Down Things fall because gravity causes objects with mass to attract one another. –We don’t yet know how or why gravity does this! But, we do know: –As objects fall they ACCELERATE (gain speed) –They do this at a CONSTANT RATE no matter what the mass of the falling object is.

The Constant Rate We use “g” as a shorthand for ACCELERATION DUE TO GRAVITY On Earth the value for ‘g’ is m/s 2 Other examples –Moon: m/s 2 –Jupiter: -26 m/s 2 –Mars: m/s 2

Falling without air resistance…

Using “g” to find changes in speed An object falls from rest. What is its velocity at the end of one second? Two seconds? Three seconds? t = 0v i = 0 m/s t = 1 sv = m/s (≈10 m/s) t = 2 sv = m/s (≈20 m/s) t = 3 sv = m/s (≈30 m/s)

Uses for “g” An object falls from rest. How far has it fallen at the end of one second? Two seconds? Three seconds? t = 0d = 0 m t = 1 sd = m (≈5 m) t = 2 s d = m (≈20 m) t = 3 sd = m (≈45 m)

Longest Freefall in History (until 2013!)

Throwing Downward An object is thrown downward from the top of a 175 meter building with an initial speed of 10 m/s. –What acceleration does it experience? m/s 2 –What is the object’s initial velocity? -10 m/s v i = -10 m/sa = m/s 2 “a” and “v i ” in SAME DIRECTION

Building Example (cont.) What is the object’s velocity as it hits the ground? v i = -10 m/s d = -175 m a = m/s 2 v f = ? How long does it take the object to hit the g round? t = ? v f 2 = v i 2 + 2ad v f 2 = 0 + 2(-9.81 m/s 2 )(-175 m) v f = m/s v f = v i + at m/s = -10 m/s + (-9.81 m/s 2 ) t t = 4.95 s

Throwing Upward A cannon fires a shot directly upward with an initial velocity of 50 m/s. –What acceleration does the cannonball experience? m/s 2 –What is the cannonball’s initial velocity? +50 m/s t = 0 s v i = +50 m/s t = 1 s v = m/s t = 2 s v = m/s “a” and “v i ” in OPPOSITE DIRECTION

Cannon (cont.) What is the object’s velocity as it reaches the top of its flight? How long does it take the cannonball to reach the top of its flight? What is the maximum height of the cannonball? 0 m/s (All objects momentarily STOP at the top of their flight) v f = v i + at 0 = +50 m/s + (-9.81 m/s 2 ) t t = 5.1 s d = v i t + ½ at 2 d = (+50 m/s)(5.1 s) + ½ (-9.81 m/s 2 )(5.1 s) 2 d = m