AP EAMCET201921 Apr 2019Evening ShiftMathematicsApplication of DerivativesActual
A ladder of 5 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate 3 m / sec . The height of the upper end (in meters) while it is descending at the rate of 4 m / sec , is
Options
- A1
- B2
- C3
- D4
Correct answer
C. 3
Step-by-step solution
It is given that the length of the ladder is: A B = 5   m From the geometry, x 2 + y 2 = 5 2 Differentiate the above equation. 2 x d y d x + 2 y d y d x = 0 x d y d x + y d y d x = 0 It is given that, d x d t = 3 , d y d t = - 4 Substitute the values in the equation I . 3   x - 4   y = 0 3 25 - y 2 - 4 y = 0 3 25 - y 2 = 4 y Squaring both sides, 9 25 - y 2 = 16 y 2 By solving, y = 3