A 10 m ladder leans against a wall. Its foot slides away from the wall at 2 m/s. How fast is the top sliding down when the foot is 6 m from the wall?
Answer and explanation
Correct answer: B. 1.5 m/s
- Step 1: Let x be the foot distance and y the top height, so x^2 + y^2 = 100. When x = 6, y = 8.
- Step 2: Differentiate with respect to time: 2x dx/dt + 2y dy/dt = 0, so dy/dt = -(x/y) dx/dt.
- Step 3: Substitute: dy/dt = -(6/8)(2) = -1.5 m/s, so the top moves down at 1.5 m/s.
Answer
1.5 m/s.
Why not the others: '1.2 m/s' uses the ratio 6/10; '2.5 m/s' uses the ratio 10/8; '2.67 m/s' inverts the ratio and uses 8/6 instead of 6/8.
Practise more Calculus and Analytical Geometry.
Free questions with an explanation for every one, and full timed Qatar Senior Secondary Certificate (Thanaweya) mock tests.
More Calculus and Analytical Geometry questions
- Evaluate the limit: lim_(x -> 0) [sin(5x) / (2x)].
- Find the derivative dy/dx of the implicit equation x^3 + y^3 = 6xy at the point (3, 3) on the Folium of Descartes.
- What is the equation of the normal line to the curve y = x^2 - 4x + 5 at the point (1, 2)?
- Evaluate the definite integral: integral from 0 to 1 of [x / (x^2 + 1)] dx.
- Find the absolute maximum value of the function f(x) = 2x^3 - 3x^2 - 12x + 1 on the closed interval [-2, 3].
- What is the total area of the finite region enclosed between the parabola y = 4 - x^2 and the line y = 0?