Question

the speed of a boat is 5 km/h in still water .it crosses a river of width 1 km along the shortest possible path in 15 min.the velocity of the river water is....?​

Answer 1

Answer:

Answer dekh le doubt hoga to puchna

Answer 2

Answer:

Velocity(v) = 3 km/hr

Explanation:

Refer to the attached image for better understanding the case.

Given;-

          Vb = 5 km/h [where Vb is velocity of boat]

             D = 1 km [where D is width of the river]

Now, for shortest possible path, the resultant path must be equal to width of the river which could only be achieved if the boat moves at ∅ angle to target.

Now,

Component of Vb in y = Vb cos∅

Component of Vb in x = Vb sin∅

Since,                    Vby = D/t

                             Vby = 1km/15 mins

                             Vby = 1km/ 1/4 h

                             Vby = 4 km/h

So, we have;

                    Vb cos∅ = 4

                          cos∅ = 4/ Vb

                          cos∅ = 4/5 [since, Vb = 5 km/h given]

                                ∅ = 37°

Then, since, for the minimum path;

                       Vb sin∅ = Vr

Hence,            Vr = 5 × sin 37°

                       Vr = 5 × 3/5

                       Vr = 3 km/h

Therefore, the velocity of the river water is 3 km/h.