A lifeguard who can swim at 1.2 m/s in still water wants to reach a dock positioned perpendicularly directly across a 550 m wide river.
1. If the current in the river is 0.80 m/s, how long will it take the lifeguard to reach the dock?
2. If instead she had decided to swim in such a way that will allow her to cross the river in a minimum amount of time, where would she land relative to the dock?
about time you did some. I passed the course in 1954.
1. To find out how long it will take the lifeguard to reach the dock, we need to consider the velocity of the lifeguard relative to the water.
In this case, the lifeguard's velocity relative to the water is the difference between her swimming speed and the velocity of the current.
Velocity relative to water = Swimming speed - Current velocity = 1.2 m/s - 0.80 m/s = 0.4 m/s
We can consider this velocity as the rate at which the lifeguard is crossing the river. To calculate the time it takes to cross the river, we divide the width of the river by the velocity.
Time = Distance / Velocity = 550 m / 0.4 m/s = 1375 seconds
Therefore, it will take the lifeguard approximately 1375 seconds to reach the dock.
2. If the lifeguard wants to cross the river in the minimum amount of time, she should swim at an angle in the river that minimizes the displacement across the river, while still accounting for the current.
In this case, we can draw a right-angled triangle with the width of the river as the base and the velocity of the current as the vertical component. The hypotenuse represents the path the lifeguard will swim.
To minimize the time taken, the lifeguard needs to aim the hypotenuse directly towards a point on the opposite bank of the river, which is equidistant from the starting point and the dock.
Thus, if the lifeguard swims in a way that minimizes the crossing distance, she will land at the point on the opposite bank directly across from her starting point and equidistant from the dock.