Question

You have a boat with a motor that propels it at vboat = 4.5 m/s relative to the water. You point it directly across the river and find that when you reach the other side, you have traveled a total distance of 27 m (indicated by the dotted line in the diagram) and wound up 14 m downstream. What is the speed of the current?

Answer 1

You have a boat with a motor that propels it at vboat = 4.5 m/s relative to the water. You point it directly across the river and find that when you reach the other side, you have traveled a total distance of 27 m (indicated by the dotted line in the diagram) and wound up 14 m downstream. What is the speed of the current?

Solution:

L = 27m – total distance;

d = 14m – distance that boat wound up downstream;

$V_{\text{boat}} = 4.5 \frac{\text{m}}{\text{s}}$ – velocity of the boat relative to the water;

$V_{\text{current}}$ – velocity of the current;

First, we can find the width of the current from the right triangle ABC:

$$h = \sqrt{L^2 - d^2}$$

Triangles ABC and BDE are similar:

$$\mathrm{ABC} \sim \mathrm{BDE}: \frac{V_{\text{boat}}}{V_{\text{current}}} = \frac{h}{d}$$ $$\frac{V_{\text{boat}}}{V_{\text{current}}} = \frac{\sqrt{L^2 - d^2}}{d}$$ $$V_{\text{current}} = \frac{d \cdot V_{\text{boat}}}{\sqrt{L^2 - d^2}} = \frac{14m \cdot 4.5 \frac{m}{s}}{\sqrt{(27m)^2 - (14m)^2}} = 2.7 \frac{m}{s}$$

Answer: speed of the current is $2.7 \frac{m}{s}$.