To solve this problem, we need to break down the boat's velocity into its components.
Let's denote the velocity of the boat with respect to the ground as V_b (in km/h) and the velocity of the river as V_r (in km/h).
We are given:
- Velocity of the boat with respect to water (V_bw) = 30 km/h
- Velocity of the river (V_r) = 6 km/h
- Width of the river (W) = 0.5 km
- Time taken to cross the river (t) = 1.25 min = 1.25/60 hours = 0.02083 hours
Now, let's calculate the component of the boat's velocity (V_bx) directed across the river.
V_bx = V_bw - V_r
V_bx = 30 km/h - 6 km/h
V_bx = 24 km/h
Therefore, the component of the boat's velocity directed across the river is 24 km/h.
Next, let's calculate the total downstream component of the boat's motion.
Distance traveled downstream (D_d) = V_bw * t
D_d = 30 km/h * 0.02083 hours
D_d = 0.625 km
Therefore, the total downstream component of the boat's motion is 0.625 km.