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]