Question

The captain of a boat wants to travel directly across a river that flows due exst with a speed of 100 m/sHe starts from the south bank of the river and heads toward the north bankThe boar has a speed of 6.10 m/s respect to the waterIn what direcuon (in degrees) should the captain steer cha is , 100 south, 270 degrees is westand

Answer 1

Answer:

86.51° North of West or 273.49°

Explanation:

Let V' = velocity of boat relative to the earth, v = velocity of boat relative to water and V = velocity of water.

Now, by vector addition V' = V + v'.

Since v' = 6.10 m/s in the north direction, v' = (6.10 m/s)j and V = 100 m/s in the east direction, V = (100 m/s)i. So that

V' = V + v'

V' =   (100 m/s)i + (6.10 m/s)j

So, we find the direction,Ф the boat must steer to from the components of V'.

So tanФ = 6.10 m/s ÷ 100 m/s

tanФ = 0.061

Ф = tan⁻¹(0.061) = 3.49°

So, the angle from the north is thus 90° - 3.49° = 86.51° North of West or 270° + 3.49° = 273.49°