Question

A river flows toward the east. Because of your knowledge of physics, you head your boat 56° west of north and have a velocity of 4.0 m/s due north relative to the shore.

(a) What is the velocity of the current?


m/s
(b) What is your speed relative to the water?


m/s

Answer 1

A river flows toward the east. Because of your knowledge of physics, you head your boat $56{}^{\circ}$ west of north and have a velocity of $4.0\mathrm{m / s}$ due north relative to the shore.

(a) What is the velocity of the current?

m/s

(b) What is your speed relative to the water?

m/s

Solution:

$\alpha = 56{}^{\circ}$ - west of north angle;

$V_{b} = 4\frac{m}{s}$ - velocity of the boat relative to the shore;

$V_{c}$ - velocity of the current;

$V_{b,c}$ - velocity of the boat relative to the water;

From the right triangle ABC:

$\sin \alpha = \frac{V_{b}}{V_{b,c}} \Rightarrow V_{b,c} = \frac{V_{b}}{\sin \alpha} = \frac{4\frac{m}{s}}{\sin 56{}^{\circ}} = 4.8\frac{m}{s}$

$\cos \alpha = \frac{V_{c}}{V_{b,c}} \Rightarrow V_{c} = V_{b,c} \cos \alpha = 4.8 \frac{m}{s} \cdot \cos 56{}^{\circ} = 2.7 \frac{m}{s}$

Answer: a) $4.8 \frac{\mathrm{m}}{\mathrm{s}}$

b) $2.7 \frac{\mathrm{m}}{\mathrm{s}}$