actice exercise an wants to row his canoe across a river. He rows so that his velocity in a southerly ection relative to the river is \( 2.5 \mathrm{~m} / \mathrm{s} \), the river is flowing East at \( 1.5 \mathrm{~m} / \mathrm{s} \) a. draw a scale diagram of these velocities and draw in the resultant velocity of the canoe b. calculate the resultant velocity of the canoe relative to the river bank

To visualize the velocities, draw a right triangle: the vertical leg represents the canoe's velocity of \(2.5 \, \text{m/s}\) south, while the horizontal leg represents the river's flow of \(1.5 \, \text{m/s}\) east. Use the Pythagorean theorem to find the resultant velocity: \[ V_{r} = \sqrt{(2.5)^2 + (1.5)^2} \approx \sqrt{6.25 + 2.25} \approx \sqrt{8.5} \approx 2.92 \, \text{m/s}. \] This resultant velocity is directed southwest and can be calculated using trigonometry: \[ \theta = \tan^{-1}\left(\frac{1.5}{2.5}\right) \approx 30.96^\circ \] from south towards east. To summarize, the resultant velocity of the canoe relative to the river bank is approximately \(2.92 \, \text{m/s}\) at an angle of about \(30.96^\circ\) east of south. This means the canoe will make a lovely diagonal path as it crosses the river, feeling like a swift adventure on the water!