a river is flowing west to east at a speed of 5 m/ minutes .in what direction should a man on the south bank of the river capable of swimming of 10 m / minutes in still water should swim to cross the river 1. in short time 2.along short path
To determine the direction in which the man should swim to cross the river, we need to consider the velocity of the river and the man's swimming speed.
1. In short time:
When crossing the river in the shortest time possible, the man should point himself directly opposite to the velocity of the river. Since the river is flowing from west to east, the man should swim in a direction opposite to east, which is westward.
2. Along the shortest path:
To cross the river along the shortest path, the man should consider the resultant velocity by adding the velocity of the river and his own swimming speed. In this case, the man can use the Pythagorean theorem to find the combined velocity.
The resultant velocity vector can be calculated using the formula:
Resultant velocity = √(velocity of river^2 + swimming speed^2)
Let's calculate it:
Resultant velocity = √(5^2 + 10^2)
Resultant velocity = √(25 + 100)
Resultant velocity = √125
Resultant velocity ≈ 11.18 m/minute
To determine the direction, the man should swim such that his resultant velocity vector is perpendicular to the river's velocity vector. In this case, it means swimming at a 90-degree angle to the river's flow.
Therefore, the man should swim northeast to counteract the river's flow and cross the river along the shortest path.
how wide is the river?
Vsw = Vs + Vw = 10 + 5i, Q1.
Tan A = Vw/Vs = 5/10 = 0.500
A = 26.6o E. of N.
Direction = 26.6o W. of N.