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?
Answers
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 mTo 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
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