A swimmer is capable of swimming at 1.4ms-¹in still water. How far downstream will he land if he swims directly across a 180m wide river? And how far will it take him to reach the other side?
crossing time = width / speed
need the speed of the current to find downstream displacement
To find the distance downstream the swimmer will land, and the time it takes to reach the other side of the river, we can use the concept of relative velocity.
Step 1: Determine the swimmer's velocity in still water.
The given velocity of the swimmer in still water is 1.4 m/s.
Step 2: Determine the velocity of the river.
From the given information, we can assume that the river is not still and it affects the swimmer's motion. However, the velocity of the river is not given in the problem statement. This missing information needs to be provided to get an accurate answer.
Step 3: Use the concept of relative velocity.
The relative velocity of the swimmer with respect to the river is the vector difference of their velocities. It is given by the vector equation:
Relative velocity = Swimmer's velocity - River's velocity
Step 4: Determine the angle between the direction of the swimmer's motion and the direction of the river's flow.
Since the swimmer intends to swim directly across the river, the angle between the swimmer's motion and the river's flow will be 90 degrees.
Step 5: Calculate the distance downstream the swimmer will land.
The distance downstream can be calculated using the formula:
Distance downstream = (Velocity of the river) * (Time taken to cross)
Step 6: Calculate the time it would take to reach the other side.
Since the swimmer's velocity and the river's velocity are both parallel to each other, the swimmer will reach the other side of the river when the distance covered is equal to 180 meters (width of the river). We can use the equation:
Time taken to reach the other side = (Width of the river) / (Velocity of the swimmer relative to the river)
Without the river's velocity, we can't proceed with the calculations. If you can provide the velocity of the river, I can help you find the answers using the mentioned steps.