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COMEDK2020MathematicsApplication of Derivatives

O A and O B are two roads enclosing an angle of 120^ . X and Y start from O at the same time. X travels along O A with a speed of 4 ~km / h and Y travels along O B with a speed of 3 ~km / h . The rate at which the shortest distance between X and Y is increasing after 1 hour is

Options

  1. A37 ~km / h
  2. B37 ~km / h
  3. C13 ~km / h
  4. D13 ~km / h

Correct answer

B. 37 ~km / h

Step-by-step solution

After time t hour distance covered by X and Y are 4 t and 3 t respectively. Now, shortest distance between X and Y after time t hour is given by aligned A B² &=O A²+O B²-2 O A O B &=(4 t)²+(3 t)²-2 4 t 3 t 120^ &=16 t²+9 t²-24 t² ( -1 2 ) &=16 t²+9 t²+12 t²=37 t² Now, d(A B) d t &= 37 aligned Rate at which the shortest distance between x and y is increasing is 37 ~km / h .

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