Answer to Question #177893 in Physics for Robert

Question

A small boat crosses from one bank of the river to its other bank and arrives at a point that is directly opposite its starting point. The engine provides a speed of 4 m / s in relation to still water. The speed of the river flow is 1.5 m / s in relation to the shore. a) At what angle was the ship directed in relation to the direction perpendicular to the course of the river? b) If the width of the river between the stated opposite points is 650 m, how long did it take the ship to cross this road? (solution-α = 22.02 °, t = 175 s)

Answer 1

The resultant velocity vector $v$ (red) must be perpendicular to the flow like in the figure below:

As we see from the image, the boat velocity of 4 m/s can be expressed as

$$4^2=1.5^2+v^2,\\\space\\ v=\sqrt{4^2-1.5^2}=3.71\text{ m/s}.$$

a) Find the angle:

$$\theta=\arctan\frac{1.5}{3.71}=22.01°.$$

b) This will take

$$t=\frac{d}v=\frac{650}{3.71}=175\text{ s}.$$