Respuesta :
Answer:
Explanation:
Given
Boat travels with a velocity of 10\ kmph w.r.t water
i.e. [tex]v_{bw}=10\hat{j}[/tex]
Velocity of water w.r.t. earth [tex]v_{we}=5\hat{i}[/tex]Therefore velocity of boat w.r.t to earth is given by
[tex]v_{bw}=v_{be}-v_{we}[/tex]
[tex]v_{be}=v_{bw}+v_{we}[/tex]
[tex]v_{be}=10\hat{j}+5\hat{i}[/tex]
magnitude of velocity [tex]v=11.18\ m/s[/tex]
He traveling at an angle of
[tex]\tan \theta =\frac{v_x}{v_y}[/tex]
[tex]\tan \theta =\frac{5}{10}[/tex]
[tex]\theta =\tan ^{-1}(0.5)[/tex]
[tex]\theta =26.56^{\circ}[/tex] east of North
(b)Now if the Boat is travelling with a speed of 10 kmph w.r.t to river due to north
therefore he must leave with some angle west of north
i.e. Boat sin component will cancel the river velocity
[tex]v\sin \theta =5[/tex]
[tex]11.18\sin \theta =5[/tex]
[tex]\theta =26.55^{\circ}[/tex]
Therefore he should be heading towards [tex]26.55^{\circ}\ West\ of\ North\ with\ a\ velocity\ of\ 11.18\ m/s[/tex]
The velocity of the boat relative to an observer standing on either bank is 11.18 m/s.
The direction of the boat is 26.56⁰ North East.
Resultant velocity of the boat
The resultant velocity of the boat is determined as follows;
V² = V₁² + V₂²
V = √(V₁² + V₂²)
V = √(10² + 5²)
V = 11.18 m/s
Direction of the boat
The direction of the boat is calculated by applying trigonometry ratio.
tanθ = V₂/V₁
tanθ = 5/10
tanθ = 0.5
θ = tan⁻¹(0.5)
θ = 26.56⁰ North East.
Learn more about relative velocity here: https://brainly.com/question/17228388
