The height of the building where a penny falls and hits the ground going 30 m/s is 45.9 m.
The height of the building can be calculated with the following equation:
[tex] v_{f}^{2} = v_{i}^{2} + 2gh [/tex]
Where:
[tex] v_{f}[/tex]: is the final speed = 30 m/s
[tex] v_{i}[/tex]: is the initial velocity = 0 (it falls from rest)
g: is the acceleration due to gravity = 9.81 m/s²
h: is the height =?
Hence, the height is:
[tex] h = \frac{v_{f}^{2} - v_{i}^{2}}{2g} = \frac{(30 m/s)^{2}}{2*9.81 m/s^{2}} = 45.9 m [/tex]
Therefore, the height of the building is 45.9 m.
Find more about freefall here:
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I hope it helps you!
