It is desired to predict the time t h that is needed for an object of mass

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It is desired to predict the time th that is needed for an object of mass m to travel downward a distance h, if gravity is the only force.

(a) If the object is stationary before release, what could you conclude about th from dimensional analysis alone?

(b) How is the dimensional analysis changed if the object is propelled downward at an initial velocity U?

(c) Derive from basic mechanics the expression for th for U ≥ 0. When put in dimensionless form, how does it compare with what you found in parts (a) and (b)?

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