6. A swimmer is capable of swimming at 12 m/s in still water. If she swims directly
across a 180m wide river whose current is 0.85 m/s.
i. How far downstream will she land?
ii. How long will it take her to reach the other side?
1. V = 12 - 0.85i = 12.03m/s[-4.05o] = 12.03m/s[4.05o] S. of E.
Tan 4.05 = d/180,
d = 180*Tan4.05 = 12.74 m. downstream.
2. d = sqrt(180^2+12.74^2) = 180.5 m.
d = V * t = 180.5
12.03 * t = 180.5,
t = seconds.
To find the answers to these questions, we need to break down the swimmer's motion into horizontal and vertical components.
i. How far downstream will she land?
To find the distance downstream, we first need to determine how long it takes for the swimmer to cross the river. Since the swimmer is swimming at an angle across the river, the current will affect her motion. The swimmer's downstream speed will be the vector sum of her swimming speed and the current velocity.
We can calculate the time it takes to cross the river using the following equation:
Time = Distance / Speed
In this case, the distance is the width of the river, which is 180m. The speed is the resultant speed, which is the vector sum of the swimmer's speed and the current velocity.
Resultant speed = √(swimmer's speed^2 + current velocity^2)
Plugging in the given values, we can calculate the resultant speed:
Resultant speed = √(12^2 + (0.85)^2) = √(144 + 0.7225) = √144.7225 ≈ 12.05 m/s
Now we can calculate the time it takes:
Time = Distance / Speed = 180m / 12.05m/s ≈ 14.95 s
Therefore, it will take the swimmer approximately 14.95 seconds to reach the other side of the river.
Next, we can find the distance downstream by multiplying the current velocity by the time:
Distance downstream = Current velocity × Time = 0.85m/s × 14.95s ≈ 12.68m
Therefore, the swimmer will land approximately 12.68 meters downstream from her starting point.
ii. How long will it take her to reach the other side?
We have already calculated the time it takes for the swimmer to reach the other side of the river, which is approximately 14.95 seconds.
Therefore, it will take the swimmer approximately 14.95 seconds to reach the other side of the river.