Answer:
The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.
Step-by-step explanation:
Here, we note the following
Let the person walking way fom the elevator be X
Let the other person going up in the elevator be Y
Therefore after 15 seconds, their positions will be;
For X, 2 ft/sec × 15 s = 30 ft away from the elevator
For Y, 7 ft/sec × 15 s = 105 ft up in the elevator
At that instant, the distance between them is given as
d² = x² + y²
= 30² +105² = 11925 ft²
d = √11925 ft² = 109.202 ft
The rate of change of the distance between the two peopl, X and Y is given as
Therefore, or
Since is given as 2 ft/sec and
= 7 ft/sec
Then