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IgorC [24]
3 years ago
7

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 v

elocity 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?
Physics
1 answer:
monitta3 years ago
3 0

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          

         

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