Question

In the calm waters of an inlet, Manon's boat moves with a velocity (speed and direction) vector \vec{b_1} = (3,4) b 1 ​ ​ =(3,4)b, start subscript, 1, end subscript, with, vector, on top, equals, (, 3, comma, 4, ). Once it enters the main river channel, however, Manon observes that it is now moving with a velocity vector \vec{b_2} = (1,1) b 2 ​ ​ =(1,1)b, start subscript, 2, end subscript, with, vector, on top, equals, (, 1, comma, 1, ).

Answer 1

Answer with Step-by-step explanation:

We are given that

$b_1=(3,4)$

$b_2=(1,1)$

We have to find the speed of river's current and the direction of current flowing.

$b=b_2-b_1=(1,1)-(3,4)=(-2,-3)$

Speed of river's current=$\mid b\mid$

Speed of river's current=$\sqrt{(-2)^2+(-3)^2}$

Speed of river's current=$\sqrt{13} m/s$

By using the formula

$\mid r\mid =\sqrt{x^2+y^2}$

Direction of current flowing,$\theta=tan^{-1}(\frac{y}{x})$

$\theta=tan^{-1}(\frac{-3}{-2})=56.3^{\circ}$

The angle lies in third quadrant therefore

$\theta=180+56.3=236.3^{\circ}$