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## Homework Statement

The ground around the Leaning Tower of Pisa one day gives way and the tower topples over. It is found from Mechanics theory that the only things that may determine the time it takes the toppling tower to fall to the ground are:

the mass (m) of the tower

the height (h) of the tower

the gravity acceleration (g).

Given that k is a dimensionless constant, the dependence of the time t for the tower to strike the ground upon m, h and g is given by:

**(a)**[tex]t=k\sqrt{\frac{g}{h}}[/tex]

**(b)**[tex]t=k\sqrt{\frac{hm}{g}}[/tex]

**(c)**[tex]t=k\sqrt{\frac{h}{g}}[/tex]

**(d)**[tex]t=km\sqrt{\frac{h}{g}}[/tex]

**(e)**[tex]t=k\sqrt{\frac{m}{g}}[/tex]

## The Attempt at a Solution

I don't recognize any of the formulas here so I can't tell which one is the correct answer. The only formula I can think of that interrelates some of these variables is [tex]h=v_y-gt[/tex] and I can replace the v by

*at*to get [tex]h=t(a-g)\Rightarrowt=\frac{a-g}{h}[/tex]. But again the resulting formula doesn't take mass into account. Can anyone help?