River Velocity from Boat and Resultant Velocity – Rankers Physics

Uncategorized: Practice Problem & Solution

A boat is sent across a river with a velocity of \(8 text{ km h}textsuperscript{-1}\). If the resultant velocity of boat is \(10 text{ km h}textsuperscript{-1}\), then velocity of river is: (1994, 93)
\(12.8 text{ km h}textsuperscript{-1}\)
\(6 text{ km h}textsuperscript{-1}\)
\(8 text{ km h}textsuperscript{-1}\)
\(10 text{ km h}textsuperscript{-1}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Resultant velocity in river-boat problems.
Formula: \(vec{v}_g = vec{v}_b + vec{v}_r\). If \(vec{v}_b\) is perpendicular to \(vec{v}_r\), then \(v_g^2 = v_b^2 + v_r^2\).
Given \(v_b = 8text{ km/h}\), \(v_g = 10text{ km/h}\).
\(v_r = sqrt{v_g^2 - v_b^2} = sqrt{10^2 - 8^2} = sqrt{100 - 64} = sqrt{36} = 6text{ km/h}\).

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