A swimmer crosses a river 300 yards wide by swimming at a constant velocity of 1 mile/hour perpendicular (that is, at right angles to) to the riverbank. The river is flowing at 3 miles per hour. What is the velocity (expressed in m/s) of the swimmer relative to an observer sitting on the shore? How far downstream will the swimmer’s landing point be from the starting point (expressed in m)? Note: Convert all variables to the metric (mks) system before performing your calculations.
add the two velocities in a right triangle. √(1^2+3^2) = √10 mi/hr
300 yds = 300/1760 = 0.17 miles
so, it will take 0.17 hours to cross the river. Since the river flows 3 times as fast as he swims, he will wind up 3*0.17 = 0.51 miles downstream.
Thank you! Do you think you can help me another problem? All I know is the formula but dont know how to plug in the numbers in it. If you dont mind.
To find the velocity of the swimmer relative to an observer on the shore, we'll first convert all the given distances and speeds to the metric system (mks).
Given:
Width of the river (W) = 300 yards = 274.32 meters (1 yard = 0.9144 meters)
Swimming velocity (V_swim) = 1 mile/hour = 0.44704 meters/second (1 mile = 1609.34 meters)
River velocity (V_river) = 3 miles/hour = 1.34112 meters/second
To calculate the velocity of the swimmer relative to the observer on the shore, we'll use the Pythagorean Theorem because the swimmer's velocity is perpendicular to the river flow.
The resultant velocity (V_resultant) can be calculated as follows:
V_resultant = √(V_swim^2 + V_river^2)
Plugging in the given values:
V_resultant = √(0.44704^2 + 1.34112^2)
V_resultant = √(0.1996 + 1.79552)
V_resultant = √1.99512
V_resultant ≈ 1.4126 meters/second
So, the velocity of the swimmer relative to an observer sitting on the shore is approximately 1.4126 meters/second.
To find how far downstream the swimmer's landing point will be from the starting point, we'll calculate the displacement caused by the river flow.
To calculate the displacement (D) caused by the river flow, we'll use the equation:
D = V_river * t
Given that the width of the river is W = 274.32 meters and the river flow velocity is V_river = 1.34112 meters/second, we need to find the time (t).
To calculate t, we'll use the formula:
t = W / V_swim
Plugging in the given values:
t = 274.32 / 0.44704
t ≈ 613.79 seconds
Now, we can calculate the displacement D caused by the river flow:
D = V_river * t = 1.34112 * 613.79 ≈ 821.71117 meters
Therefore, the swimmer's landing point will be approximately 821.71117 meters downstream from the starting point.