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A boat, whose speed in still water is 2.50 m/s, must cross a 285-m wide river and arrive at a point 118m upstream from where it starts. To do so, the pilot must head the boat at a 45.0 degrees upstream angle. What is the speed of the rivers current?

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Blacklash

The figure shows the arrangement of system

The velocity of boat can be resolved in to two

     Horizontal component  = vcos θ = 2.50 cos 45 = 1.768 m/s

     Vertical component  = vsin θ = 2.50 sin 45 = 1.768 m/s

   Due to horizontal component the boat arrive arrives upstream,

           Total horizontal velocity =  1.768 - Vr, where Vr is the velocity of river.

  Total time taken to cross the river = width of river/ Vertical component of velocity

                         t = 285/1.768 = 161.20 seconds

So 118 meter is traveled at a velocity of 1.768-Vr in 161.20 seconds

That is           118 = (1.768-Vr)*161.20

                     1.768 - Vr =0.732

                         Vr = 1.036 m/s

So velocity of river flow =1.036 m/s

Ver imagen Blacklash
onyebuchinnaji

The speed of the river current with respect to the boat is 1.036 m/s.

The given parameters;

  • speed of boat, [tex]v_b[/tex] = 2.5 m/s
  • width of the river, w = 285 m
  • distance upstream, d = 118 m
  • direction of the pilot, θ = 45⁰

A sketch of the river flow;

                              118 m

                  |-------------------------------|

                  ↓

          285 ↓

                  ↓

The vertical and horizontal component of the velocity is calculated as follows;

[tex]v_y = vsin(\theta) = 2.5 \times sin45 = 1.768 \ m/s \\\\v_x = vcos(\theta) = 2.5 \times cos45 = 1.768 \ m/s \\\\[/tex]

The time taken for the boat to cross the river is calculated as follows;

[tex]t = \frac{y}{v_y} \\\\t = \frac{285}{1.768} \\\\t = 161.2 \ s[/tex]

The total horizontal velocity of the boat and the river is calculated as;

[tex]v_x = 1.768 - V_r\\\\(1.768-V_r)t = 118\\\\1.768 - V_r = \frac{118}{t} \\\\1.768 - V_r = \frac{118}{161.2} \\\\1.768 - V_r = 0.732\\\\V_r = 1.768 - 0.732\\\\V_r = 1.036 \ m/s[/tex]

Thus, the speed of the river current with respect to the boat is 1.036 m/s.

Learn more here:https://brainly.com/question/12923196

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