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 40 feet long, but can stretch up to 120 feet. They both start from the same location. Allyson moves 10 ft/sec and Adrian moves 6ft/sec in the directions indicated. (If a coordinate system is used, assume that the girls" starting position is located at (x,y)=(0,0) and that Allyson and Adrian move in the positive y and negative x directions, respectively. Let one unit equal one foot.) Where are the two girls located after 2 seconds?

Answer 1

Allyson would be 20 ft to the north (positive y-direction) from the starting point, and Adrian would be 12 ft to the west (negative x-direction) from the starting point.

Step-by-step explanation:

To find the locations of Allyson and Adrian after 2 seconds, we need to determine how far each of them has moved in that time.

Allyson's speed is 10 ft/sec, so after 2 seconds, she would have traveled 10 ft/sec x 2 sec = 20 ft to the north (positive y-direction).

Adrian's speed is 6 ft/sec in the negative x-direction, so after 2 seconds, he would have traveled 6 ft/sec x 2 sec = -12 ft to the west (negative x-direction).

Since they both started from the same location, Allyson and Adrian would end up at coordinates (0 + 0, 0 + 20) = (0, 20). Allyson would be 20 ft to the north (positive y-direction) from the starting point, and Adrian would be 12 ft to the west (negative x-direction) from the starting point.