a swimmer is capable of swimming at 1.4ms in still water how far downstream will he land if he sweams directy across a 180M wide river
Well, if the swimmer swims at 1.4 m/s, it sounds like he's really making a splash! Now, let's calculate how far downstream he will land if he swims directly across a 180 m wide river.
Assuming the river's current is not a joke, we'll need to take it into account. Let's say the current of the river is 0.5 m/s.
We can use the formula "distance = speed × time" to find the time it takes for the swimmer to cross the river. Since the swimmer is swimming directly across, the distance he needs to cover is still 180 m.
So, the time it takes can be calculated as: time = distance / (swimming speed + current speed).
time = 180 m / (1.4 m/s + 0.5 m/s)
time ≈ 100 seconds (approximately)
Now that we know the time it takes to cross the river, we can find how far downstream the swimmer will land by calculating: distance downstream = current speed × time.
distance downstream = 0.5 m/s × 100 s
distance downstream = 50 meters.
So, the swimmer will land approximately 50 meters downstream from where he started. It seems like he'll need to do a little extra swimming to make it back to the starting point!
To determine how far downstream the swimmer will land, we need to consider the velocity of the river's current in addition to the swimmer's speed. Let's assume the river's current is 0.8 m/s flowing in one direction.
First, we can find the swimmer's effective speed when swimming across the river. This can be calculated using the Pythagorean theorem, where the hypotenuse represents the swimmer's resultant velocity.
The vertical component of the swimmer's velocity (v_vertical) is equal to the river's current velocity since they cancel each other out when swimming perpendicular to the current. Thus, v_vertical = 0.8 m/s.
To find the horizontal component of the swimmer's velocity (v_horizontal), we can use the following formula:
v_horizontal^2 = swimmer's speed^2 - v_vertical^2
v_horizontal^2 = (1.4 m/s)^2 - (0.8 m/s)^2
v_horizontal^2 = 1.96 m^2/s^2 - 0.64 m^2/s^2
v_horizontal^2 = 1.32 m^2/s^2
Taking the square root of both sides, we get:
v_horizontal = √(1.32 m^2/s^2)
v_horizontal ≈ 1.15 m/s
Now, we can calculate the time it takes for the swimmer to cross the river:
Time = Distance / Velocity
Time = 180 m / 1.15 m/s
Time ≈ 156.52 s
Since the swimmer's effective speed includes both the river's current and their own speed, we can calculate their downstream distance using the formula:
Distance downstream = v_water × Time
Distance downstream = (0.8 m/s) × (156.52 s)
Distance downstream ≈ 125.22 m
Therefore, the swimmer will land approximately 125.22 meters downstream when swimming directly across the 180-meter wide river.
To determine how far downstream the swimmer will land, we need to consider two things: the speed of the swimmer and the speed of the river current.
Let's assume the swimmer swims perpendicular to the river current, directly across the river. In this case, the swimmer's velocity will be a combination of their swimming speed and the speed of the river current.
Given that the swimmer's speed in still water is 1.4 m/s, we need to determine the speed of the river current. Let's assume the speed of the river current is represented by v_c.
To find the speed of the river current, we can use the fact that the swimmer is not displaced horizontally while swimming across the river. This means that the relative velocity of the swimmer with respect to the ground should be zero.
Relative velocity of the swimmer with respect to the ground:
v_s - v_c = 0
Since v_s represents the swimmer's velocity in still water, we can write the equation as:
1.4 m/s - v_c = 0
Solving for v_c:
v_c = 1.4 m/s
Now that we know the speed of the river current, we can determine the distance the swimmer will be displaced downstream. The time it takes to swim across the river can be calculated using the following equation:
Time = Distance / Velocity
In this case, we can calculate the time it takes for the swimmer to cross the river using the width of the river (180 m) and the swimmer's velocity in still water (1.4 m/s):
Time = 180 m / 1.4 m/s
Calculating the time:
Time = 128.57 s
Now that we know the time it takes to cross the river, we can determine the distance the swimmer will be displaced downstream by multiplying the time by the speed of the river current:
Distance downstream = 128.57 s * 1.4 m/s
Calculating the distance downstream:
Distance downstream = 180 m
Therefore, the swimmer will land approximately 180 meters downstream from their starting point when swimming directly across a 180-meter wide river.
it will take him 180/1.4 = 128.57 seconds to get across.
How far downstream he'll go depends on the speed of the water.