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1-1-5 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 -9.81 m/s2

• Other examples– Moon: -1.62 m/s2

– Jupiter: -26 m/s2

– Mars: -3.75 m/s2

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 = 0 vi = 0 m/s

t = 1 s v = -9.81 m/s (≈10 m/s)

t = 2 s v = -19.62 m/s (≈20 m/s)

t = 3 s v = -29.43 m/s (≈30 m/s)

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Uses for “g”• An object falls from rest. How far has it fallen at

the end of one second? Two seconds? Three seconds?

t = 0 d = 0 m

t = 1 s d = -4.905 m (≈5 m)

t = 2 s d = -19.62 m (≈20 m)

t = 3 s d = -44.145 m (≈45 m)

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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?• -9.81 m/s2

– What is the object’s initial velocity?• -10 m/s

vi = -10 m/sa = -9.81 m/s2

“a” and “vi” in SAME DIRECTION

Building Example (cont.)• What is the object’s velocity as it hits the ground?

• vi = -10 m/s• d = -175 m• a = -9.81 m/s2

• vf = ?

• How long does it take the object to hit the ground?• t = ?

vf2 = vi

2 + 2advf

2 = 0 + 2(-9.81 m/s2)(-175 m)vf = -58.6 m/s

vf = vi + at-58.6 m/s = -10 m/s + (-9.81 m/s2) 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?• -9.81 m/s2

– What is the cannonball’s initial velocity?

• +50 m/s

t = 0 svi = +50 m/s

t = 1 sv = +40.19 m/s

t = 2 sv = +30.38 m/s

“a” and “vi” in OPPOSITE DIRECTION

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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)

vf = vi + at0 = +50 m/s + (-9.81 m/s2) t

t = 5.1 s

d = vit + ½ at2

d = (+50 m/s)(5.1 s) + ½ (-9.81 m/s2)(5.1 s)2

d = +127.4 m