If you can swim in still water at 0.5m/s, the shortest time it would take you to swim from bank to bank across a 20m wide river, if the water flows downstream at a rate of 1.5m/s, is most nearly:

42.55 seconds

Explanation:

Check attached file for the diagram.

Vr= velocity of the river, if the water flows downstream, which is equal to 1.5m/s(from the question), Vb= my velocity at angle alpha which is perpendicular to the x-axis, and c= distance to swim from river bank to the other river bank.

Therefore, the shortest time to be taken to swim or cross the river,t=river with width of C÷ vertical component Vj.

Note that (vector) Vj= (vector)Vr+(vector)Vb.

Also, alpha must be maximum and for that to happen it must have a value of one(1).

Hence, time taken to cross the river,t= C/Vb× sin (alpha).

t= 20m÷ 0.5 ×sin 90.

t= 20÷ 0.47.

t= 42.55 seconds.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.