A 220-m-wide river flows due east at a uniform speed of 3.8m/s. A boat with a speed of 7.8m/s relative to the water leaves the south bank pointed in a direction 35o west of north. What is the (a) magnitude and (b) direction of the boat's velocity relative to the ground

a) = 6.6m/s

b) = 125.15°

Explanation:

Speed of the boat =3.8m/s

width of the both = 220m

speed of boat relative to water = 3.8m/s, 35°

Relative Velocities V₀ = V₁ + V₂

V₀ = Velocity of the boat relative to ground

V₁ = Velocity of the boat relative to river

V₂ = Velocity of the river relative to ground

V₁ = Velocity of the boat relative to river = -4.47i + 6.55j

V₀ = Velocity of the boat relative to ground

= (-4.47i + 6.55j) + (3.8i)

= (0.67i + 6.55j)m/s

Magnitude V₀

/V₀/ = √(0.67² + 6.55²)

= 6.6m/s

b)

Direction of the boat relative to ground

cosθ= -V₂ / /V₀/

cosθ = -3.8 / 6.6

θ = 125.15°

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