Please explain all detail. Other questions similar to this problem on this websi

Question

Please explain all detail. Other questions similar to this problem on this website havent explained it well enough for me to understand the problem. The figure illustrates the apparatus for a tightrope walker. Two poles are set x = 60 feet apart. Starting at the lowest point, the tightrope walker moves up the rope at a steady rate of 2 ft/sec. If the rope is attached y = 40 feet up the pole, express the height h of the walker above the ground as a function of time t. (Hint: Let d denote the total distance traveled along the wire. First express d as a function of t, and then h as a function of d. Assume the tightrope walker begins moving up the rope at t = 0.)

Explanation / Answer

Draw a 2ft foot pole and then a 40 ft pole 60 feet apart.

Then cut both poles to the ground so you have a triangle. thetightrope walkerwalks up thehypotenuse.

Let d(t) be the distance the tightrope walker has walked long the hypotenuse.

Let h(t) be the height the tightrope walker has gone straight up.

The angle the tightrope walker climbs is sin(a) = 38/60 (1)

The tightrope walker goes up the rope at 2 ft/sec.
So d(t) = 2t. (2)

At time t, sin(a) = h(t)/d(t) (3)

Using (1) , (2) and (3) ==>38/60= h(t)/2t ==> h(t) = 2t*38/60

So h(t) = 19t/15


The angle the tightrope walker climbs is sin(a) =38/60

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