College Physics by Openstax Chapter 2 Problem 10

Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon’s orbit increases by 3.84×106 m(1%)?

Solution:

From the formula v‾=ΔxΔt\overline{v}=\frac{\Delta x}{\Delta t}, we can solve for Δt \Delta t as follows

Δt=Δxv‾=3.84×106 m4 cm/year×100 cm1 m=96 000 000 years=96.0×106 years  (Answer)\begin{align*} \Delta \text{t} & = \frac{\Delta x}{\overline{v}} \\ & = \frac{3.84\times 10^6\:\text{m}}{4\:\text{cm/year}}\times \frac{100\:\text{cm}}{1\:\text{m}} \\ & =96\:000\:000\:\text{years} \\ & =96.0\times 10^6\:\text{years} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

It will take about 96 million years.

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