A boat travels at 15 m/s in a direction 45° east of north for an hour. The boat then turns and travels at 18 m/s in a direction 5° north of east for an hour.
What is the magnitude of the boat's resultant velocity? Round your answer to the nearest whole number.
I mis
What is the direction of the boat's resultant velocity? Round your answer to the nearest whole degree.
north of east
Done
Intro

 v = 31 m, / s;  θ = 1 north- east

Explanation

One of the easiest ways to solve these problems is to work with the components of vectors.

Let's set a reference system where the x axis coincides with the West - East direction

Let's use trigonometry

        cos 45 = v₁ₓ / v₁

        sin 45 = v_{1y} / v₁

        v₁ₓ = v1 cos 45

        v_{1y} = v₁₁ sin 5

         v₁ₓ = 15 cos 45 = 10.6 m / s

         v   _{1y} = 15 sin 45 = 10.6 m / s

         sin 5 = v₂ₓ / v₂

        cos 5 = v_{2y} / v₂

        v₂ₓ = v2 sin 5

         v_{2y}= v2 sin 5

         v₂ₓ = 18 sin 5 = 1.569 m / s

         v_{2yₓ} = 18 cos 5 = 17.93 m / s

Let's look for the speed in each axis

          vₓ = v₁ₓ + v₂ₓ

          vx = 10.6 + 1.569

          vx = 12.17 m / s

          v_y = v_{1y} + v_{2y}

          v_y = 10.6 + 17.93

          v_y = 28.53 m / s

to find the velocity let's use the Pythagorean theorem

           v =

           v = √ (12.17² + 28.53²)

           v = 31.02 m / s

approaching the nearest ether

           v = 31 m / s

b) we use trigonometry

          tan θ = vy / vx

           θ = tan -1

          θ = tan vy / vx

          θ = tan-1 17.93 / 12.17

         θ= 1.47

the closeΕst integer is

 θ = 1 north- east

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