Question

allyson and adrian have decided to connect their ankles with a bungee cord; one end is tied to each person's ankle. the cord is 30 ft long but stretches to 90 ft. they both start from the same location. allyson moves 10 ft/sec and adrian moves 8 ft/sec in the directions indicated. a) after 2 seconds will the slack in the cord be used up? b)determine when the bungee cord first becomes tight, where are the girls located? c) when will the bungee cord first touch the corner of the building? (using similar triangles)

Answer 1

the directions indicated are shown here

Answer 2

a) after 2 seconds Allyson will have gone 2*10=20 ft, Adrian 2*8=16 ft. The cord connecting them will have to be at least
\[\sqrt{20^2+16^2}=25.6\]
Therefore the slack will not be used up

Answer 3

b) The equation would be
\[30=\sqrt{(10x)^2+(8x)^2}=x \sqrt{164}\]
which yelds
\[x=30/4\sqrt{41}=15/2\sqrt{41}\approx 2.3426 s\]