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° nor

Question

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

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Dulcie 5 years 2021-07-30T03:44:53+00:00 1 Answers 36 views 0

Answers ( )

  1. King
    0
    2021-07-30T03:46:05+00:00
    Reply

    Answer:

     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 = \sqrt{v_x^2 +v_2^2 }

               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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