Tightrope walker Refer to Exercise Starting at the lowest point, the tightrope walker move...

Tightrope walker Refer to Exercise 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 30 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.)

Length of a tightrope The figure illustrates the apparatus for a tightrope walker. Two poles are set 50 feet apart, but the point of attachment P for the rope is yet to be determined.

(a) Express the length L of the rope as a function of the distance x from P to the ground.

(b) If the total walk is to be 75 feet, determine the distance from P to the ground.

EXERCISE