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Home Continuous Functions Related Rates Examples Example 2
 
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Example 2

A 10 foot ladder is propped against a wall. The bottom end is being pulled along the floor away from the wall at a constant rate of 2ft/sec. Find the rate at which the top of the ladder is sliding down the wall when the bottom end is 5 ft from the wall.

Warning:
Although the bottom end of the ladder is being moved at a constant rate, the rate, at which the top end moves wil vary with time.

The diagram is shown in Figure 3.2.2.

03_continuous_functions-22.gif

Figure 3.2.2

Step 1

t = time,

x = distance of the bottom end from the wall,

y = height of the top end above the floor.

Step 2

dx/dt = 2, x2 + y2 = 102 = 100.

Step 3

We differentiate both sides of x2 + y2 = 100 with respect to t.

03_continuous_functions-14.gif , whence 03_continuous_functions-15.gif

Step 4

Set x = 5 ft and solve for dy/dt. We first find the value of y when

x = 5

x2 + y2 = 100, y =03_continuous_functions-16.gif

Then we can solve for dy/dt,

03_continuous_functions-17.gif

03_continuous_functions-23.gif

The sign of dy/dt is negative because y is decreasing.

Home Continuous Functions Related Rates Examples Example 2

Last Update: 2006-11-15