(Solved): please show work 10) Relative Velocity: A river flows due north with a speed of \( 2.40 \mathrm{~m} ...

10) Relative Velocity: A river flows due north with a speed of \( 2.40 \mathrm{~m} / \mathrm{s} \). A man rows a boat across the river. His velocity relative to the water is \( 4.20 \mathrm{~m} / \mathrm{s} \) due east. The river is \( 1000 \mathrm{~m} \) wide. (Assume 3 sig. figs in this problem.) Use standard relative velocity vector notation (i.e., \( \vec{v}_{\psi} \) represents the velocity of the boat relative to the water) throughout this problem. Show your work in symbols first (as always). a) Sketch a diagram showing the velocity vectors, and label each vector. b) Write the vector addition equation showing how the three velocity vectors are related as vectors. c) What is his velocity relative to the earth (magnitude and direction)? d) How much time is required to cross the river? e) How far north of his starting point will he reach the opposite bank?