A boatman is crossing the river of width h = 80 m from point A to point B. He steers the boat at an angle α = 3 7 ∘ to the shoreline all the time. The river speed is 'u' because of which the

Question

A boatman is crossing the river of width h = 80 m from point A to point B. He steers the boat at an angle $α = 3 7^{\circ}$ to the shoreline all the time. The river speed is 'u' because of which the boat is always drifting and finally lands at a distance $ℓ = 60 m$ on the other bank as shown in the figure. Find the speed of boat relative to ground (in m/s) if its speed v with respect to the river is 12 m/s.

TestHub · Accepted Answer

Across the river: h = ( v sin α ) t ⇒ 80 = 12 × 5 3 ​ t ⇒ t = 9 100 ​ s . Along the river: 60 = ( u − 12 × 5 4 ​ ) × 9 100 ​ ⇒ u = 15 m/s . v b / g ​ = ( 15 − 5 48 ​ ) 2 + ( 5 36 ​ ) 2 ​ = 5. 4 2 + 7. 2 2 ​ = 9 m/s . Answer: 9.

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