You are watching the Chicago marathon from your friend's apartment, 100 feet above the street. A runner passes the building at 11 feet/sec. Let d denote the distance between the base of the building and the runner, and let h denote the distance between you and the runner. How fast is the distance between you and the runner changing 20 seconds after she passed the building?
did you get it?
I got 220, did you?
I think mines is wrong though
To find how fast the distance between you and the runner is changing, we need to determine the rate at which the distance is changing with respect to time.
Let's use the Pythagorean theorem to relate the distances involved. According to the theorem, the square of the hypotenuse (h) is equal to the sum of the squares of the other two sides (d and 100). So, we have the equation:
h^2 = d^2 + 100^2
Differentiating both sides of this equation with respect to time (t), we get:
2h * dh/dt = 2d * dd/dt
Simplifying the equation, we can cancel out the 2's and rewrite it as:
h * dh/dt = d * dd/dt
Now, we can solve for dh/dt, which represents how fast the distance between you and the runner is changing.
At the given time, d represents the distance between the base of the building and the runner, and we are given that dd/dt (the rate at which d is changing) is 11 feet/sec. We also know that h is 100 feet.
Plugging these values into the equation, we have:
(100 feet) * (dh/dt) = (d) * (11 feet/sec)
Now, we need to find the value of d at the given time. Since we haven't been given any specific information about the position of the runner at this time, we don't have enough information to determine the exact value of d.