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

Following are the solution to this question:

Explanation:

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

`\to (12)/(l)= (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 = ( (6.5)/(12))l \\\\`

Calculating the Derivative of the above value:

`\to (dx)/(dt) = ((6.5)/(12)) (dl)/(dt)\\\\\to (dl)/(dt) = ((12)/(6.5)) (dx)/(dt)\\\\\to (dx)/(dt) = 2 \\\\ \to (dl)/(dt) = ( (12)/(6.5) * 2)`

`=(24)/(6.5) \\\\= (48)/(13) \ (ft)/(sec)`

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

`\to (48)/(13) - 2 \\\\ \to (48-26)/(13) \\\\ \to (22)/(13) \ (ft)/(sec)`