Chapter 8.1, Problem 23PPSE

Solution

To find the mass of rocket in terms of $F$ and $d$ .

Mass is given by the equation $m=F{d}^2$ .

Given information:

Force $F$ of gravity on a rocket varies directly with its mass $m$ and inversely with the square of its distance $d$ from earth.

Concept:

Inverse variation: When one of the given variables increases with decrease in other variable, then it is inverse variation or vice versa.

It can be represented as:

  $xy=k$ (Product of variables remains constant)

Direct variation: When one variable increases with increase in other variable, or decreases with decrease in other variable then it is direct variation.

It can be represented as:

  $k=\frac{x}{y}$ (Ratio of variable remains constant)

Calculation:

From the given statement:

  $F=\frac{m}{d^2}$

Now, mass is,

  $\begin{array}{l}F=\frac{m}{d^2}\\ m=F{d}^2\end{array}$

Conclusion:

Hence, mass is given by the equation $m=F{d}^2$ .