Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t...
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Transcript of Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t...
![Page 1: Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t Advanced – s = v 1 t + ½at² – v 2 2 − v 1 2 = 2as.](https://reader036.fdocuments.us/reader036/viewer/2022082411/56649dc75503460f94abcb0c/html5/thumbnails/1.jpg)
Height
![Page 2: Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t Advanced – s = v 1 t + ½at² – v 2 2 − v 1 2 = 2as.](https://reader036.fdocuments.us/reader036/viewer/2022082411/56649dc75503460f94abcb0c/html5/thumbnails/2.jpg)
Formulas• Basic– a = ( v2 − v1 ) / t
– = ( vv̄� 1 + v2 ) / 2– s = tv̄� ∙
• Advanced– s = v1t + ½at²
– v22 − v1
2 = 2as
![Page 3: Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t Advanced – s = v 1 t + ½at² – v 2 2 − v 1 2 = 2as.](https://reader036.fdocuments.us/reader036/viewer/2022082411/56649dc75503460f94abcb0c/html5/thumbnails/3.jpg)
How Long Does it Take an Object to Fall 80 meters?
• v1 = 0 m/s• s = − 80 m• a = − 10 m/s²• t = ??
• s = v1t + ½at²
• s = 0 + ½at²• 2s = at²• 2s/a = t² = • −160m/(−10m/s²) = 16 s²• t = 4 seconds
![Page 4: Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t Advanced – s = v 1 t + ½at² – v 2 2 − v 1 2 = 2as.](https://reader036.fdocuments.us/reader036/viewer/2022082411/56649dc75503460f94abcb0c/html5/thumbnails/4.jpg)
Suppose we throw the object upward and it rises to a height of 80 meters.
• v2 = 0 m/s• s = 80 m• a = − 10 m/s²• t = ??
• s = v1t + ½at²
• v1 and t are both unknown
• Use v22 − v1
2 = 2as
• v22 − 2as = v1
2
• 0 − 2(−10m/s2 80 m) = v∙ 12
• 1600 m2/s2 = v12
• v1 = 40 m/s
a = (v2 − v1 ) / t
t = (v2 − v1 ) / a
= (0 − 40m/s )/−10m/s2
= 4 seconds
![Page 5: Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t Advanced – s = v 1 t + ½at² – v 2 2 − v 1 2 = 2as.](https://reader036.fdocuments.us/reader036/viewer/2022082411/56649dc75503460f94abcb0c/html5/thumbnails/5.jpg)
A Trip Up and Down
t = 0 secv = +40 m/s
t = 4 secv = 0 m/s
t = 8 secv = −40 m/s
= + 20 m/sv̄� = − 20 m/sv̄�
![Page 6: Height. Formulas Basic – a = ( v 2 − v 1 ) / t – v̄ = ( v 1 + v 2 ) / 2 – s = v̄ ∙ t Advanced – s = v 1 t + ½at² – v 2 2 − v 1 2 = 2as.](https://reader036.fdocuments.us/reader036/viewer/2022082411/56649dc75503460f94abcb0c/html5/thumbnails/6.jpg)
Up And Down• When thrown in the air,
objects take as long to go up as to come down.
• v22 − v1
2 = 2as • Net displacement (up and down) s = 0• v2
2 − v12 = 0 v2
2 = v12
• v1 = − v2 v1
is up, v2 is down
Neglecting Friction