A 240-m-wide river flows due east at a uniform speed of 4.8m/s. A boat with a speed of 7.2m/s relative to the water leaves the south bank pointed in a direction 33o west of north. What is the (a) magnitude and (b) direction of the boat's velocity relative to the ground

Respuesta :

Answer:

a)[tex]V_b=6.1m/s[/tex]

b) [tex]\alpha=66.59 \textdegree[/tex]

Explanation:

From the question we are told that:

Width of river  [tex]W=240[/tex]

River speed [tex]V_r=4.8m/s[/tex]

Boat speed [tex]V_b=7.2m/s[/tex]

Boat Direction [tex]\theta= 33 \textdegree[/tex]

Generally the equation for Boat Velocity Vector is mathematically given by

By Resolving Co-Planar forces

 [tex]\=V_{br}=\=V_b-\=V_r[/tex]

 [tex]\=V_{br}=-7.2sin33i+7.2cos33j[/tex]

Therefore

 [tex]\={V_{b}}=\={V_{br}}-\={V_r}[/tex][tex]\=V_{b}=\=V_{br}-\=V_r[/tex]

 [tex]\=V_{b}=4.8-7.2sin33i+7.2cos33j[/tex]

 [tex]\=V_b=4.8-7.2 sin33 i+7.2 cos33j[/tex]

Therefore Magnitude of Boat velocity is

 [tex]V_b=\sqrt{(4.8-7.2sin33)^2+(7.2cos33j)^2}[/tex]

 [tex]V_b=6.1m/s[/tex]

b)

Generally the equation for Direction of the boat's velocity is mathematically given by

 [tex]\alpha=tan^{-1}\frac{y}{x}[/tex]

 [tex]\alpha=tan^{-1}\frac{7.2cos33)}{4.8-7.2sin33}[/tex]

 [tex]\alpha=66.59 \textdegree[/tex]

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