a man wishes to swin across a river 600 m wide. If can swim at the rate of 4 km/hr in still water and the river flows at 2 km/hr. Then in what direction must he swim to reach a point exactly opposite to the starting point bnd when will he reach it ?

Can u show the figure of it?

His velocity relative to water must have a 2 km/hr component upstream. The component across the stream is therefore

sqrt[4^2 - 2^2) = 3.464 km/hr

He must swim at an angle arcsin(2/4) = 30 degrees relative to straight-across.

The time to swim across will be

T = 0.6/3.464 = 0.1732 hr = 10.4 minutes

To determine the direction in which the man must swim to reach a point exactly opposite his starting point, we need to consider the velocity of the swimmer and the velocity of the river current.

Let's break down the problem into components:

1. Velocity of the man in still water: 4 km/hr
2. Velocity of the river current: 2 km/hr

To find the direction the man should swim:

1. Determine the net velocity of the man relative to the ground by considering the vector addition of his velocity in still water and the velocity of the river current.
Net velocity = Velocity of the man in still water + Velocity of the river current
= 4 km/hr + 2 km/hr
= 6 km/hr

2. The man should swim in the opposite direction of the net velocity to counteract the effect of the river current.
Therefore, he should swim in the direction opposite to the direction of the river current, which is towards the starting point.

To determine the time it will take for the man to reach the point exactly opposite his starting point, we can use the formula:

Time = Distance / Speed

3. Calculate the time required:
Distance = 600 m (since the river is 600 m wide)
Speed = 6 km/hr

Convert the distance into kilometers: 600 m = 0.6 km

Time = 0.6 km / 6 km/hr
= 0.1 hr

Since 1 hour = 60 minutes, and 0.1 hr * 60 minutes/hr = 6 minutes,

The man will reach the point exactly opposite his starting point in 6 minutes.

To determine the direction the man should swim and when he will reach the opposite point, we need to break down the problem and calculate the effective velocity.

Let's denote the following:
- The width of the river is 600 meters.
- The man's speed in still water is 4 km/hr.
- The river's speed is 2 km/hr.

To calculate the effective velocity, we need to consider the man's velocity relative to the ground and the river's velocity. We'll use vector addition to find the resulting velocity.

1. Find the velocity of the man with respect to the ground:
The man's speed in still water is 4 km/hr, so his velocity vector in still water is 4 km/hr in the direction he swims.

2. Find the velocity of the river:
The river is flowing at a speed of 2 km/hr, so the river's velocity vector is 2 km/hr in the direction of the river flow.

3. Combine the man's velocity and the river's velocity:
In order to reach the opposite point, the man needs to swim in a direction that counteracts the effect of the river's flow.
Since the man's velocity vector is opposing the river's velocity vector, we subtract them:
Resulting velocity vector = Man's velocity vector - River's velocity vector.
Resulting velocity = 4 km/hr - 2 km/hr = 2 km/hr.
So, the effective velocity of the man relative to the ground is 2 km/hr in the opposite direction of the river's flow.

4. Calculate the time required to cross:
The total distance the man needs to cross is 600 meters.
The effective velocity is 2 km/hr, which is equivalent to (2 km/hr * 1000 m/km * 1 hr/3600 sec) = 0.556 m/s.
Using the formula time = distance / velocity, we can calculate the time it takes to cross:
time = 600 m / 0.556 m/s =~ 1079.14 seconds.

Therefore, the man should swim in the opposite direction of the river's flow, and it will take approximately 1079.14 seconds to reach the point exactly opposite to the starting point.