Question

Problem A man wishes to cross a river which
boat whose velocity with respect to water is
In flowing at a certain speed. Man uses a motor
more than speed of flow. Minimum possible time
the boat takes to cross the river is t, but drift
along the length of river is x. When boat takes
shortest route to cross the river, then it takes
timely. Find the velocity of boat with respect to
water.​

Answer 1

Answer:

Case 1: If the man crosses the river in minimum time he should move perpendicular to bank or normal to the direction of water flow.

Let ∣

v

→

m.w

∣=v and ∣

v

→

w

∣=u

Time to cross river, t

1

=10=

v

d

⇒d=10v,

x=ut

1

⇒120u=u×10⇒u=12mmin

−1

Case 2: If the man crosses river taking the shortest route, the drift should be zero. Time to cross river,

t

2

=12.5=

v

2

−u

2

d

From case 1, d=10v and v=12ms

−1

12.5=

v

2

−12

2

10v

⇒v=20ms

−1

solution

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