A long distance swimmer is able to swim through still water at 4km/hr. She wishes to swim from Port Angeles, WA due north to Victoria, B.C., a distance of 50km. An ocean current flows through the Strait of Juan de a from west to east at 3km/hr. In what direction should she swim to make the crossing along a straight line between the two cities?
Draw a vector diagram. The velocity with respect to ground has to point directly across from PA to Victoria. It is also the vector sum of the water speed and the swimmer's velocity.
Use trig functions to get the angle you need.
the thing is. i don't know what to do witht the 50km cuz its different units from the 3km/hr and the 4km/hr
velocity, speed, and inertia!I DON'T GET IT!!
To determine the direction in which the long distance swimmer should swim to make the crossing along a straight line between Port Angeles, WA and Victoria, B.C., we need to consider the vectors of the swimmer's velocity and the ocean current.
The swimmer's velocity is given at 4 km/hr directly northward. Meanwhile, the ocean current flows from west to east at a velocity of 3 km/hr.
To calculate the direction of the swimmer's actual velocity, we can subtract the vector of the ocean current from the vector of the swimmer's velocity.
Given that the swimmers velocity vector is northward, it can be represented as a vector <0, 4> km/hr. Similarly, the ocean current vector can be represented as <3, 0> km/hr.
Subtracting the ocean current vector from the swimmer's velocity vector, we get:
<0, 4> km/hr - <3, 0> km/hr = <-3, 4> km/hr
Therefore, the swimmer's actual velocity, accounting for the ocean current, is in the direction represented by the vector <-3, 4> km/hr.
To determine the direction in terms of compass direction, we can use trigonometry. The angle of the resulting vector can be found by calculating the arctan of the ratio of the components:
angle = arctan(4/-3)
Using a calculator, we find that the angle is approximately -53.13 degrees.
Now, considering that the swimmer wants to go northward (0 degrees), she should adjust her direction by 53.13 degrees to the west (left), counteracting the eastward direction of the ocean current.
Therefore, she should swim in a direction approximately northwest to counterbalance the effect of the ocean current and reach Victoria, B.C. directly.
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