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 feet long, but can stretch up to 90 feet. They both start from the same location. Allyson moves 20 ft/sec and Adrian moves 12 ft/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
(a) Where are the two girls located after 2 seconds?
Allyson (x,y)
Adrian (x,y)
(c) Determine when the bungee cord first becomes tight; i.e., there is no slack in the line. (Round your answer to one decimal place.) in sec
Where are the girls located when this occurs? (Round your answers to one decimal place as needed.)
Allyson (x,y)
Adrian (x.y)
(d) When will the bungee cord first touch the corner of the building? (Hint: Use a fact about "similar triangles." Round your answer to one decimal place as needed.) in sec
I am very lost
file:///C:/Users/grant/Downloads/qrcode_www.webassign.net.png
the graph iam look at
To solve this problem, we need to break it down into steps and calculations. Let's go through each part step by step:
(a) To determine the girls' locations after 2 seconds, we need to calculate their displacements. We can use the formula:
Displacement = Speed * Time
For Allyson:
Displacement = 20 ft/sec * 2 sec = 40 ft in the positive y-direction.
For Adrian:
Displacement = 12 ft/sec * 2 sec = 24 ft in the negative x-direction.
Therefore, after 2 seconds:
Allyson is located at (x, y) = (0, 40) [positive y-direction].
Adrian is located at (x, y) = (-24, 0) [negative x-direction].
(c) To determine when the bungee cord becomes tight, we need to find the time at which the distance between the two girls is equal to the length of the bungee cord (30 ft).
The distance between the two girls can be calculated using the distance formula from coordinate geometry:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Since they start at the same location, their initial positions are (0,0).
Thus, the distance between them at any time t is:
Distance = √[(Adrian's x-position)^2 + (Allyson's y-position)^2]
Plugging in the given values:
Distance = √((-24)^2 + (40)^2) = √(576 + 1600) = √2176
We need to find the time when this distance is equal to the length of the bungee cord (30 ft).
√2176 = 30
To solve for t, we square both sides of the equation:
2176 = 30^2
2176 = 900t^2
t^2 = 2176/900
t^2 = 2.4178
Taking the square root of both sides:
t = √2.4178
t ≈ 1.55 seconds
Therefore, the bungee cord first becomes tight at approximately 1.6 seconds.
To determine where the girls are located when this occurs, you can substitute the value of t back into the displacement formulas from part (a). The positions will be:
Allyson: (x, y) = (0, 1.55 * 20) ≈ (0, 31)
Adrian: (x, y) ≈ (1.55 * -12, 0) ≈ (-18.6, 0)
(d) To find when the bungee cord touches the corner of the building, we can use the fact about "similar triangles." The triangle formed by the girls' positions and the corner of the building is similar to the triangle formed by their initial positions and the corner of the building.
The ratio of the lengths of the corresponding sides in similar triangles is equal. In this case, it means the ratio of the distances of the girls from the building corner at any time will be equal to the ratio of their initial distances from the building corner.
The initial distance of Allyson from the corner of the building is 0 ft, as she starts from the origin, (0,0).
The initial distance of Adrian from the corner of the building can be calculated using the Pythagorean theorem:
Adrian's initial distance = √((-24)^2 + 0^2) = √576 = 24 ft.
So, to find when the bungee cord first touches the corner of the building, we need to solve for t in the equation:
Distance of Allyson from the building corner = Distance of Adrian from the building corner
This equation will be:
Allyson's displacement = Adrian's initial displacement
20t = 24
Solving for t:
t = 24/20
t = 1.2 seconds
Therefore, the bungee cord will first touch the corner of the building at approximately 1.2 seconds.
The positions of the girls at this time will be:
Allyson: (x, y) = (0, 1.2 * 20) = (0, 24)
Adrian: (x, y) = (1.2*-12, 0) ≈ (-14.4, 0)
I hope this explanation helps you understand the steps involved in solving each part of the problem!
cannot access files on your computer. But, clearly, after t seconds,
Allyson is at (0,20t)
Adrian is at (-12t,0)
and the distance between them is 4√34 t
(a) 4√34 * 2 = ____
(c) 4√34 t = 30
(d) no idea where the building is