justin is trying to swim across a 300m wide river with a 1.50m/s current north if he heads directly west for the opposite bank with an average speed of 1.00 m/s how far down stream will he be carried
To find out how far downstream Justin will be carried, we can use the concept of relative velocity.
The velocity of the current is 1.50 m/s north, and Justin is swimming west at 1.00 m/s. The resulting velocity (relative velocity) will be the vector sum of these two velocities.
Using the Pythagorean theorem, we can find the magnitude of the relative velocity:
V_relative = sqrt((1.50)^2 + (1.00)^2) = sqrt(2.25 + 1) = sqrt(3.25) = 1.80 m/s
Since Justin is swimming west while the current is pushing him north, the direction of the relative velocity will be at an angle of arctan(1.50/1.00) = arctan(1.50) = 56.31 degrees north of west.
Now that we have the relative velocity, we can calculate how far downstream Justin will be carried in the time it takes him to swim across the river.
Time to swim across the river = 300m / 1.00 m/s = 300 s
Distance downstream = V_relative * time
Distance downstream = 1.80 m/s * 300 s = 540 m
Therefore, Justin will be carried 540 meters downstream by the current while trying to swim across the river.