11. A passenger on a boat moving at 1.70m/s on a still lake walks up a flight of stairs at a speed of 0.60m/s The stairs are angled at 45^circ pointing in the direction of motion as shown.What is the velocity of the passenger rel- ative to the water?

To find the velocity of the passenger relative to the water, we need to consider both the velocity of the boat and the velocity of the passenger walking up the stairs.<br /><br />Given:<br />- Velocity of the boat: $1.70 \, m/s$<br />- Velocity of the passenger walking up the stairs: $0.60 \, m/s$<br />- Angle of the stairs: $45^\circ$<br /><br />The velocity of the passenger relative to the water can be found using the Pythagorean theorem, as the velocities form a right triangle.<br /><br />The velocity of the passenger relative to the water is given by:<br /><br />$v_{\text{relative}} = \sqrt{(v_{\text{boat}})^2 + (v_{\text{stairs}})^2}$<br /><br />$v_{\text{relative}} = \sqrt{(1.70 \, m/s)^2 + (0.60 \, m/s)^2}$<br /><br />$v_{\text{relative}} = \sqrt{2.89 + 0.36}$<br /><br />$v_{\text{relative}} = \sqrt{3.25}$<br /><br />$v_{\text{relative}} \approx 1.80 \, m/s$<br /><br />Therefore, the velocity of the passenger relative to the water is approximately $1.80 \, m/s$.