Please Help-Calculus- related rate problem?

Question

I have no idea how to solve those problems.
Please help.
Thanks!

a.Determine the approproated "ralated rates"
b.Solve the problem and interpret your result.

1.A ten foot ladder is leaning against a wall. suppose that the foot of the ladder is being pilled out at a rate of 3feet per second. how fast is the top of the ladder sliding down the wall when the foot of the laddet is 8feet from the wall.


2.An airplane flying 390 feet per second at an altitude of 5000 fett flew directly over an observer. If the plane is flying away the observer, how fast is the distance from the observer to the airplane changing at the time when the airplane is 13000feet from the observer?


3. A baseball diamond is a 90 ft by 90 ft square. A player runs from first to second base at a speed of 22 feet per second. How fast is the player's distance from third base changing when he is halfway between first and second base?

Answer 1

(1) Remember Pythagorean Theorem?
a²+b² = c² Now re-write it as
x²+y² = 10² From the problem, you're looking for
dy/dt when you're given dx/dt, so differentiate with respect to time to get
2x dx/dt + 2y dy/dt = 0 and
dy/dt = (-2x dx/dt)/(2y) Now, when the base of the ladder is 8 feet from the wall, the top of the ladder is
√(10²-8²) = 6 feet from the ground. At this point, it's just plug 'n play to get
dy/dt = (-2*(8)*3)/(2*6) = -4 ft/sec.

Now..... **You** get busy and do the rest of them. Math is like any other sport; You don't get good at it by watching someone else play ☺


Doug