Tracy swims across a stream of width 40.0 m in 33.0 s when there is no current. She takes 59.0 s to cover the same distance when there is a current. Find the speed of the river current.
Magnitude of velocity, v = 40/33 m/s
Construct the relative velocity vectors which form a right-triangle. The angle α, the angle between her orientation and the line perpendicular to the shore, is given by
cos(α)= 33/59
sin(α)=sqrt(1-(33/59)²)
and finally,
the current speed, c = v sin(α)
.532 m/s
Bri is inncorect, the answer is aprx. 1.00251 m/s
To find the speed of the river current, we need to first calculate the speed at which Tracy swims without any current. We can use the formula:
speed = distance / time
When there is no current, Tracy swims across the stream with a speed of:
speed_without_current = distance / time_without_current
where distance = 40.0 m and time_without_current = 33.0 s.
Using the given values, we can calculate the speed without any current:
speed_without_current = 40.0 m / 33.0 s
Next, we need to find Tracy's speed relative to the ground when there is a current. We can use the same formula:
speed_with_current = distance / time_with_current
where distance = 40.0 m and time_with_current = 59.0 s.
Using the given values, we can calculate the speed with the current:
speed_with_current = 40.0 m / 59.0 s
Finally, we can find the speed of the river current by subtracting Tracy's speed without the current from her speed with the current:
speed_of_current = speed_with_current - speed_without_current
Substituting the values we calculated earlier, we get:
speed_of_current = (40.0 m / 59.0 s) - (40.0 m / 33.0 s)
Now we can calculate the exact value for the speed of the river current.