Jon
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The document summarizes solving a physics problem about the rate at which the foot of a falling ladder is moving away from a wall. It provides the information given, which is that the top of a 13-foot ladder is slipping down a wall at 2 feet per second when it is 5 feet above the ground. It outlines the steps to set up and solve the kinematic equations to find that the rate the foot is moving away from the wall is 5/6 feet per second.
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Jon
- 2. THE QUESTION A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 5 ft above the ground?
- 3. What we know We know that: Y=5 X=12 Dy/dt=-2 Dx/dt= ? 13 5 We also know that an equation for this diagram is X² + Y² = 13² 12 We found out that X= 12 because of the Pythagorean Theorem.
- 4. Step 1: Take the derivative of the equation X ² + Y² = 13² 2x(dx/dt) + 2y(dy/dt) =0
- 5. Step 2: Plug in The derivative is: 2x(dx/dt) + 2y(dy/dt) =0 Y=5 X=12 Dy/dt=-2 2(12)(dx/dt) + 2(5)(-2) =0
- 6. Step 3: Solve for dx/dt 2(12)(dx/dt) + (2)(5)(-2) = 0 24(dx/dt) – 20 = 0 24(dx/dt) = 20 So….. dx/dt = ……...
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