A boat sails across a river with a velocity of 10 km/hr. If resultant boat velocity is 14 km/hr, then what is the velocity of river water?a)17.20 km/hrb)10 km/hrc)9.79 km/hrd)4.88 km/hrCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given data:
Speed of the boat in still water (B) = 14 km/hr
Speed of the boat across the river (V) = 10 km/hr

Let the velocity of the river be 'R'.

The velocity of the boat can be resolved into two components:
1. Velocity of the boat in the direction of the river flow (Vr)
2. Velocity of the boat perpendicular to the river flow (Vp)

Hence,
B = Vr + Vp

Given, V = 10 km/hr

As the boat is sailing at an angle to the river flow, the velocity of the boat perpendicular to the river flow is given by:
Vp = V x sinθ
where θ is the angle between the boat's velocity and the river flow.

In this case, θ = 90°, as the boat is sailing perpendicular to the river flow.

Therefore, Vp = V x sin90° = V

Hence, B = Vr + V

Also, given B = 14 km/hr

Substituting the values, we get:
14 = Vr + 10
Vr = 14 - 10 = 4 km/hr

Now, the velocity of the river can be calculated as follows:
Vr = R
4 = R
R = 4 km/hr

Therefore, the velocity of the river water is 4 km/hr, which is option (c).

Answer

√(14^2-10^2)

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