A swimmer is capable of swimming at 1.4m/s in still water. Calculate the following.
i. How far downstream will he land if he swims directly across 180m wide river?
ii. How long will it take him to the other side.
give me hint for solving it
129
13.6
Tell me how to solve it
To calculate the distance downstream where the swimmer will land and the time it will take him to the other side, we need to consider the swimmer's velocity and the river's current.
Given:
Swimmer's velocity (in still water) = 1.4 m/s
River width = 180 m
i. To calculate how far downstream the swimmer will land, we need to find the component of the swimmer's velocity perpendicular to the river's flow. We can use the concept of vector addition to calculate this distance.
Let's assume the swimmer's velocity is represented as v_s (1.4 m/s) and the river's current velocity is represented as v_r.
Since the swimmer is swimming directly across the river, the angle between the swimmer's velocity and the river's current is 90 degrees.
The component of the swimmer's velocity perpendicular to the river's flow can be calculated using trigonometry:
v_perpendicular = v_s * sin(theta)
where theta is the angle between the swimmer's velocity and the river's current (which is 90 degrees in this case).
v_perpendicular = 1.4 * sin(90)
v_perpendicular = 1.4 * 1
v_perpendicular = 1.4 m/s
Now, we can calculate the distance downstream using the time it takes to cross the river:
Distance downstream = v_perpendicular * time
Since the swimmer travels at a constant velocity, the time to cross the river is given by:
time = (river width) / (swimmer's velocity in still water)
time = 180 m / 1.4 m/s
time = 128.57 seconds (rounded to two decimal places)
Distance downstream = 1.4 m/s * 128.57 s
Distance downstream = 179.99 meters (rounded to two decimal places)
Therefore, the swimmer will land approximately 179.99 meters downstream from his starting position.
ii. The time it will take the swimmer to reach the other side (time to cross the river) is 128.57 seconds (as calculated in part i).
Hence, it will take approximately 128.57 seconds for the swimmer to reach the other side of the river.