A 10-foot ladder leans against a vertical wall. If the bottom of the ladder slides away from the wall at ft/s, how fast is the top of the ladder sliding down the wall when the bottom is ft from the wall?
Answer and explanation
Correct answer: A.
- Step 1: Relate the variables using the Pythagorean theorem: .
- Step 2: When , solve for : .
- Step 3: Differentiate with respect to time : .
- Step 4: Substitute known values: .
- Step 5: The rate at which the ladder slides down is .
Answer
.
Why not the others: '2.0 ft/s' assumes both velocities are equal; '1.2 ft/s' computes incorrectly; '2.5 ft/s' divides 10 by 4.
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