A monkey on a raft is crossing a river that flows to the east at 8.0m/s. His top paddling speed is 12.0m/sec. He points due south and attempts to cross. If the river is 120m wide, how far downstream will he end up when he reaches the other side?

Respuesta :

The relation of uniform movement allows to find the result for the distance that descended when crossing the river is:

           d = 180 m

Given parameters

  • The velocity of the river [tex]v_r[/tex] = 8.0 m / s towards the East
  • The speed of the monkey [tex]v_m[/tex] = 12.0 m / s towards the south
  • River width x = 120 m

To find

  • Distance downstream when crossing.

Velocity is a vector magnitude, it has modulus and direction, therefore vector algebra must be used.

The velocities are constant, let's use the uniform motion relation.

           v = [tex]\frac{d}{t}[/tex]  

In the attached we have a diagram of the movement.  Let's calculate the time to cross the river.

          [tex]v_r = \frac{x}{t}[/tex]  

            [tex]t= \frac{x}{v_r}[/tex]  

            t = [tex]\frac{120}{8.0}[/tex]  

            t = 15 s

The time is a scalar it is the same for the two movements, let's find how much it has descended in this time.

          [tex]v_m = \frac{d}{t}[/tex]  

           d = [tex]v_m t[/tex]  

           d = 12.0  15

           d = 180 m

In conclusion, using the uniform motion relationship we can find the result for the distance that descended when crossing the river is:

           d = 180 m

Learn more here: brainly.com/question/11298125

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