A) 1 km/h
B) 2 km/h
C) 3 km/h
D) 4 km/h
Correct Answer: C
Solution :
Key Idea: For shortest path velocity of boat must be perpendicular-to the river velocity. We know that, We know that, \[\text{Velocity = }\frac{\text{distance}}{\text{time}}\] Also, 1 h = 60 min \[\therefore \] \[15\,,min\,=\frac{1}{4}\text{h}\] Now, relative velocity of boat is , \[{{v}_{b}}=\frac{d}{t}=\frac{1}{1/4}\,=4\,\text{km/h}\] Velocity of boat must be perpendicular to the velocity of river while crossing the river in shortest path. Hence, relation for velocity of river water is \[v_{br}^{2}=v_{b}^{2}+v_{w}^{2}\] \[\Rightarrow \] \[{{5}^{2}}={{4}^{2}}=v_{w}^{2}\] \[\Rightarrow \]\[v_{w}^{2}=\sqrt{{{5}^{2}}-{{4}^{2}}}\,=3\,\text{km/h}\]You need to login to perform this action.
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