Respuesta :
Answer:
Explanation:
Given
Ship A velocity is 40 mph and is traveling 35 west of north
Therefore in 2 hours it will travel [tex]40\times 2=80 miles[/tex]
thus its position vector after two hours is
[tex]r_A=-80sin35\hat{i}+80cos35\hat{j}[/tex]
similarly B travels with 20 mph and in 2 hours
[tex]=20\times 2=40 miles
Its position vector[tex]r_B=40sin80\hat{i}+40cos80\hat{j}[/tex]
Thus distance between A and B is
[tex]r_{AB}=\left ( -40sin80-80sin35\right )\hat{i}+\left ( 80cos35-40cos80\right )\hat{j}[/tex]
[tex]|r_{AB}|=\sqrt{\left ( -40sin80-80sin35\right )^2+\left ( 80cos35-40cos80\right )^2}[/tex]
[tex]|r_{AB}|=103.45 miles[/tex]
Velocity of A
[tex]v_A=-40sin35\hat{i}+40cos35\hat{j}[/tex]
Velocity of B
[tex]v_B=20sin80\hat{i}+20cos80\hat{j}[/tex]
Velocity of A w.r.t B
[tex]v_{AB}=v_A-v_B[/tex]
[tex]v_{AB}=\left ( -20sin80-40sin35\right )\hat{i}+\left ( 40cos35-20cos80\right )\hat{j}[/tex]
