Height

Formulas• Basic– a = ( v2 − v1 ) / t

– = ( vv̄� 1 + v2 ) / 2– s = tv̄� ∙

• Advanced– s = v1t + ½at²

– v22 − v1

2 = 2as

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

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

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�

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