When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m?

Explanation

Time t \propto \sqrt{d}, so \frac{t_1}{\sqrt{d_1}} = \frac{t_2}{\sqrt{d_2}}. We have \frac{4}{\sqrt{78.4}} = \frac{t_2}{\sqrt{122.5}}. Solving for t_2: t_2 = 4 \times \sqrt{\frac{122.5}{78.4}} = 4 \times \sqrt{\frac{1225}{784}} = 4 \times \frac{35}{28} = 4 \times 1.25 = 5 seconds.

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