Let's solve each part step by step: --- ### **Given:** - Width of river, \( d = 150\, \text{m} \) - Boat speed in still water, \( v_b = 4.\, \text{m/s} \) (north) - Speed of river current, \( v_c = 2.\, \text{m/s} \) (east) --- ## (a) **How long does the boat take to reach the other side?** The time to cross depends only on the speed **perpendicular** to the river banks (north direction), not on the current. \[ t = \frac{d}{v_b} \] \[ t = \frac{150\, \text{m}}{4.\, \text{m/s}} = 37.5\, \text{s} \] **Answer (a):** \[ \boxed{37.5\, \text{s}} \] --- ## (b) **How far downstream does it drift?** The downstream drift depends on the **current** and the **time** it takes to cross. \[ \text{Downstream drift} = v_c \times t \] \[ = 2.\, \text{m/s} \times 37.5\, \text{s} = 75\, \text{m} \] **Answer (b):** \[ \boxed{75\, \text{m}} \] --- ## (c) **What is the magnitude of the boat’s velocity relative to the shore?** The boat's velocity relative to the shore is the vector sum of its velocity in still water (north) and the river's velocity (east): \[ v_{\text{relative}} = \sqrt{v_b^2 + v_c^2} \] \[ = \sqrt{(4.\, \text{m/s})^2 + (2.\, \text{m/s})^2} \] \[ = \sqrt{16 + 4} \] \[ = \sqrt{20} \] \[ \approx 4.47\, \text{m/s} \] **Answer (c):** \[ \boxed{4.47\, \text{m/s}} \] --- ## **Summary Table** | Part | Answer | |------|---------------| | (a) | 37.5 s | | (b) | 75 m | | (c) | 4.47 m/s | Let me know if you need the direction for (c) or any other details!