Struggling to swim

Noah's velocity with respect to the river is 2 m/s east. Because his velocity is constant, we can use the equation:

$d=vt$

where d is the distance traveled, t is the time since starting, and v is the velocity. Solving for t we get:

$t=\frac{d}{v}$

$t=\frac{10 m}{2 m/s}$

$t=5 s$

We know that it took Noah 5 seconds to swim across the river, so Noah was also being pushed down the river by the current for 5 seconds. Thus, we can use the river's velocity of 4 m/s in the original constant velocity equation to find the distance Noah traveled downstream:

$d=(5 s)(4 m/s)$

$d=\boxed{20 m}$

Therefore, Noah reaches the other side 20 meters downstream from his starting point.

Going at 2m/s across a 10m stretch will take 5 seconds. 5x4=20

We have two vectors, one which is him swimming east at 2m/s and another of the river pushing him down at 4m/s, both of these are independent

To cross the river with the east vector it will take 5 seconds

Plug that in for the river, and the river, at 4m/s for 5 seconds will push him 20 meters

He crosses the 10 m wide river with velocity 2 m/s, so he takes time $= \frac{Distance}{Speed} = \frac{10}{2} = 5$ sec.

Now, speed of river is 4 m/s, so while crossing river in 5 sec, Noah gets displaced downstream $= Speed\times Time = 4\times 5 = \boxed{20}$ m

Noah swims 2m/s due east wrt to the river

Time he will take to reach the other bank = 10 / 2 = 5 econds

Downstream displacement will be caused by the flow of the river

Hence, the downstream distance travelled = speed of river downstream * time of swimming

                     = 4 * 5 m

                     = 20 m

Since the river is 10 m wide, Noah would take 10/2 = 5 seconds to cross it.

In this much time, the river would have swept him 4*5 = 20m.

20

Here the component of velocity in the direction of river flow must be 4 m/s and in the direction of the width of the river the component is 2 m/s.So it takes Noah 10/2=5 s to cross the river and in this time he drifts 5*4=20 m along the river.