Transcript UpAndDown.pptx

Height
Formulas
• Basic
–
–
–
a =
v̄ =
s =
( v2 − v1 ) / t
( v1 + v2 ) / 2
v̄ ∙ t
• Advanced
–
–
s = v1t + ½at²
v22 − v12 = 2as
How Long Does it Take an Object
to Fall 80 meters?
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v1
s
a
t
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s = v1t + ½at²
s = 0 + ½at²
2s = at²
2s/a = t² =
−160m/(−10m/s²) = 16 s²
t = 4 seconds
=
0 m/s
= − 80 m
= − 10 m/s²
=
??
Suppose we throw the object upward
and it rises to a height of 80 meters.
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v2
s
a
t
= 0 m/s
= 80 m
= − 10 m/s²
= ??
• s = v1t + ½at²
• v1 and t are both unknown
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•
•
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Use v22 − v12 = 2as
v22 − 2as = v12
0 − 2(−10m/s2 ∙ 80 m) = v12
1600 m2/s2 = v12
v1 = 40 m/s
a = (v2 − v1 ) / t
t = (v2 − v1 ) / a
= (0 − 40m/s )/−10m/s2
= 4 seconds
A Trip Up and Down
t = 4 sec
v = 0 m/s
v̄ = + 20 m/s
t = 0 sec
v = +40 m/s
v̄ = − 20 m/s
t = 8 sec
v = −40 m/s
Up And Down
• When thrown in the air,
Neglecting Friction
objects take as long to go
up as to come down.
• v22 − v12 = 2as
• Net displacement (up and down)  s = 0
• v22 − v12 = 0
 v22 = v12
• v 1 = − v2
v1 is up,
v2 is down