Question

At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?

Answer 1

Answer:

Following are the solution to this question:

Step-by-step explanation:

Please find the complete question and the graph in the attached file.

$\to \frac{12}{l}= \frac{5.5}{l-x}\\\\\to 12(l - x) = 5.5l\\\\\to 12l - 12x = 5.5l\\\\\to 12l -5.5l = 12x\\\\\to 6.5l =12x\\\\\to 12x = 6.5l \\\\\to x = ( \frac{6.5}{12})l$

Calculating the Derivative of the above value:

$\to \frac{dx}{dt} = (\frac{6.5}{12}) \frac{dl}{dt}\\\\\to \frac{dl}{dt} = (\frac{12}{6.5}) \frac{dx}{dt}\\\\\to \frac{dx}{dt} = 2 \\\\ \to \frac{dl}{dt} = ( \frac{12}{6.5} \times 2)$

        $=\frac{24}{6.5} \\\\= \frac{48}{13} \ \frac{ft}{sec}$

by subtracting the rate of the shade from that of the man:

$\to \frac{48}{13} - 2 \\\\ \to \frac{48-26}{13} \\\\ \to \frac{22}{13} \ \frac{ft}{sec}$