Answer to Question #279347 in Mechanics | Relativity for btch

Question

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.2 m/s due east. The river is 800 m wide. (a) What is his velocity (magnitude and direction) relative to the earth? (b) How much time is required to cross the river? (c) How far south of his starting point will he reach the opposite bank?

Answer 1

a)

$v=\sqrt{v_m^2+v_r^2}=4.65~\frac ms,$

$\theta=\arctan\frac{v_r}{v_m}=25.5°$S to E,

b)

$t=\frac l{v_m}=190 ~s,$

c)

$s=v_r t=380~m.$