Question

speed of a man in water is 5 km ther, man
tories to cross a vive filowing towards
cast at 3km/hr of width Toom.
find the Shortest time in which man crosses
river.
Aut what angle from flow velocity man
Should swim to reach directly opposite Point
Man starts swimming forum Point A making
S3 angle with flow velocity. Find the
Position where he will reach also find
the time.​

Answer 1

$\huge \underline \green{\sf{ Answer :- }}$

a. Velocity of man with respect to river water, v=5kmh−1. This is greater than the river flow velocity. Therefore, he can cross the river directly (along the shortest path or no drift condition from flow velocity). The angle of swim,

θ=2π+sin−1(vu)

= 90o+sin−1(vu)

= 90o+sin−1(53)

=90o+37o

= 127o w.r.t. the river flow or 37o w.r.t. the perpendicular in upstream direction

• b. Resultant velocity or velocity of mass will be vm = v2 −u2

= 52−32

=4kmh−1

$\small \underline {\sf{In \ the \ direction \ perpendicular \ to \ the \ river \ flow. }}$

• c. time taken to cross the river

t = d/ v2−u2d

= 1km / 4kmh ^ −1

= 1 / 41h

$\small \underline {\sf{ q \ = \ 15min}}$

Answer 2

Answer:

a. Velocity of man with respect to river water, v=5kmh−1. This is greater than the river flow velocity. Therefore, he can cross the river directly (along the shortest path or no drift condition from flow velocity). The angle of swim,

θ=2π+sin−1(vu)

= 90o+sin−1(vu)

= 90o+sin−1(53)

=90o+37o

= 127o w.r.t. the river flow or 37o w.r.t. the perpendicular in upstream direction

b. Resultant velocity or velocity of mass will be vm = v2 −u2

= 52−32

=4kmh−1

\small \underline {\sf{In \ the \ direction \ perpendicular \ to \ the \ river \ flow. }}

In the direction perpendicular to the river flow.

c. time taken to cross the river

t = d/ v2−u2d

= 1km / 4kmh ^ −1

= 1 / 41h

\small \underline {\sf{ q \ = \ 15min}}

q = 15min