Chapter MPS, Problem 8.9MPS

To determine

To find when the women’ winning jump will be higher than that of men.

Answer to Problem 8.9MPS

  $254$ Years.

Explanation of Solution

Given:

In 1928, women’s jump was $62.5$ inches while men’s jump was $76.5$ inches after that women’s jump increased $0.38\%$ about and the men’s jump increased at $0.3\%$

Calculation:

Let the time be $t$ years when the women’ winning jump will be higher than that of men.

So, according to the question-

  $\begin{array}{l}62.5{\left(1+\frac{0.38}{100}\right)}^t>76.5{\left(1+\frac{0.3}{100}\right)}^t\\ \Rightarrow 0.816993\times {1.0038}^t>{1.003}^t\\ \Rightarrow {1.0038}^t>1.224\times {1.003}^t\\ \Rightarrow t>253.514\end{array}$

Therefore, $254$ years will be taken when the women’ winning jump will be higher than that of men.