A river is flowing from west to east at a speed of 8m/min, a man on the south bank of the river , capable of swimming at 20m/min in still water, wants to swim across the river in the shortest time. He should swim in a direction of a) due north b) 30 degree east of north c) 30 degree west of north d) 60 degree east of north
X = Vw = 8 m/min.
Y = Vs = 20m/min.
Tan A = Y/X = 20/8 = 2.500.
A = 68.2o N. of E. = 21.8o E. of N.
Direction = 21.8o W. of N. to offset
affect of the wind.
C is the closest answer.
A river is flowing from west to east at a speed of 8m/min, a man on the south bank of the river , capable of swimming at 20m/min in still water, wants to swim across the river in the shortest time. He should swim in a direction of a) due north b) 30 degree east of north c) 30 degree west of north d) 60 degree east of north
Answer will be (A) - due north
To find out the shortest time for the man to swim across the river, we need to consider the velocity of the river and the swimming speed of the man in still water.
Let's analyze each option:
a) If the man swims in a due north direction, he will have to swim against the river's current. This means that his effective speed will be reduced by the speed of the river. Therefore, his effective speed will be 20m/min - 8m/min = 12m/min. Therefore, it will take him the longest time to swim across the river in this direction.
b) If the man swims 30 degrees east of north, his effective speed can be calculated using vector addition. Let's break the man's swimming speed into its northward and eastward components:
- Northward component: 20m/min * cos(30°)
- Eastward component (against the river's current): 20m/min * sin(30°) - 8m/min
Using these components, we can calculate the effective speed using vector addition. The effective speed is the square root of the sum of the squares of the northward and eastward components:
Effective speed = sqrt((20m/min * cos(30°))^2 + (20m/min * sin(30°) - 8m/min)^2)
c) If the man swims 30 degrees west of north, his effective speed can be calculated using a similar approach as in option b). The only difference is that the eastward component will work in favor of the man's motion:
Effective speed = sqrt((20m/min * cos(30°))^2 + (20m/min * sin(30°) + 8m/min)^2)
d) If the man swims 60 degrees east of north, his effective speed can be calculated using the same approach:
Effective speed = sqrt((20m/min * cos(60°))^2 + (20m/min * sin(60°) - 8m/min)^2)
By comparing the effective speeds calculated for options b, c, and d, we can determine which direction will result in the shortest time for the man to swim across the river.