Question

A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10 m/s due north relative to the water.(a) What is the velocity of the boat relative to the shore?(b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?

Answer 1

Answer:

a

   $u = 10.11 \ m/s$

b

   $x = 44.996 \ m$    

Explanation:

From the question we are told that    

        The velocity of the river due east is  $v = 1.150i \ m /s$

        The velocity of the boat due north is  $v_1 = 10j \ m/ s$

         The width of the river is  $d = 300 \ m$

Generally the velocity of the boat relative to the shore

           $u = \sqrt{v^2 + v_1^2}$

=>        $u = \sqrt{1.50 ^2 + 10^2}$

=>        $u = 10.11 \ m/s$

Generally direction of the boat relative to the shore is mathematically represented as

           $tan \theta = \frac{v}{v_1}$

=>        $\theta = tan^{-1}[ \frac{v}{v_1}]$

=>        $\theta = tan^{-1}[ \frac{1.5}{10}]$

=>        $\theta = 8.53^o$

Generally the distance covered by the boat in the direction of flow of the river before reaching the north shore is mathematically represented as

             $x = d* tan(\theta )$

=>          $x = 300 * tan(8.53)$

=>         $x = 44.996 \ m$