Section 2.29  Interactive checkpoint: penny drop  
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You drop a penny off Taiwan’s Taipei 101 tower, which is 509 meters tall. How long does it take to hit the ground? Ignore air resistance, consider down as negative, and the ground as having zero height.
 
 

Answer:

t = s

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Diagram  [Hide]

Variables  [Hide]

Fill in the known values.

Down is negative and the ground is the origin.

Variable

Value
acceleration

a = m/s2

initial velocity

vi = m/s

final velocity

vf

displacement

Δx = m

elapsed time

t

I think I'm done. I need help. Show the correct values.
 
Strategy  [Hide]
  1. Select an equation that contains the variables you are given, and the one you want to calculate. Avoid equations with two unknowns.
Physics principles and equations  [Hide]

vf = vi + at

Δx = vit + ½at2

vf2 = vi2 + 2aΔx

Δx = ½(vi + vf)t

Step-by-step solution   [Hide]
2

Select the equation that will help you calculate the elapsed time.

Enter initial velocity

A “dropped” penny has no initial velocity.

Δx = ( m/s)t + ½at2

Solve for elapsed time

Δx = ½at2

2Δx / a = t2

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Enter values

Pay attention to signs. Down is negative, which means both the acceleration and the displacement are negative.

t = [2( m) / ( m/s2)]1/2

Multiply and divide

t = [ s2]1/2

Take the positive square root

t = s
 
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