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)

Question

Mathematics

Sophia Lucas

23 November, 15:11

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)

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Answers (1)

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Madilynn Herman · Answer 1

Assuming the two move in opposite directions

a)

Distance between the two = 10x - (-8x); x is the time in seconds

D = 18x

At x = 2,

D = 36 ft

This is greater than the length of the cord so it will not be slack.

b) The cord is tight when the girls' distance is 30 ft

30 = 18x

x = 1.67 seconds

Allyson will be:

10 x 1.67 = 16.7 feet from her starting position

Adrian will be:

8 x 1.67 = 13.3 feet from her starting position

Part c requires the figure.