OnlineCBT
Physics · MOTION IN A PLANE
हिन्दीA motorboat is heading due north at a speed of \( 25\text{ km/h} \), and the water current in that region is moving at \( 10\text{ km/h} \) in the direction of \( 60^\circ \) east of south. Calculate the magnitude of the resultant velocity of the motorboat relative to the shore.
Correct answer · Option C
\( 5\sqrt{19}\text{ km/h} \)
Explanation
Boat velocity \( \mathbf{v}_b = 25\hat{\mathbf{j}} \). Current velocity \( \mathbf{v}_c = 10\sin 60^\circ \hat{\mathbf{i}} - 10\cos 60^\circ \hat{\mathbf{j}} = 5\sqrt{3}\hat{\mathbf{i}} - 5\hat{\mathbf{j}} \). Net velocity \( \mathbf{v} = 5\sqrt{3}\hat{\mathbf{i}} + 20\hat{\mathbf{j}} \). Magnitude \( v = \sqrt{(5\sqrt{3})^2 + 20^2} = \sqrt{75 + 400} = \sqrt{475} = 5\sqrt{19}\text{ km/h} \).
