A zipline steel cable is being constructed a reality televis

A zip-line steel cable is being constructed a reality television show. The high end of the zip-line is attached to the top of a 50 foot pole while lower end is anchored at ground level to a stake 50 feet from the base. (a) Find the angle of elevation of the zip-line. (b) Find the number of feet of steel cable needed for the zip-line (c) A contestant takes 6 seconds to reach the ground from the top of the zip-line. At what rate is the contestant moving down the line? At what rate is the contestant dropping vertically?

Solution

a) angle of elevation =tan^-1(50/50)

angle of elevation =tan^-1(1)

angle of elevation =45^o

b)length of steel cable needed =[50²+50²]

length of steel cable needed =502

length of steel cable needed =70.71 feet

c)rate of contestant moving down the line =70.71/6 =11.785ft/s

rate of contestant dropping vertically =50/6 =8.333 ft/s