Question

A man crosses the river with a boat. if he crosses the river in minimum time he takes 10 minutes with a drift of 120 m. if he crosses the river with the shortest path he takes 12.5 minutes. assuming velocity of river

Answer 1

vx^2+vy^2=v^2 where v is magnitude of man's velocity


vy=12m/min since its the shortest path
so vx=root(v^2-12^2)


for the shortest time
d=10*v


10v=12.5*root(v^2-12^2)


v=root(12.5^2*10^2/(12.5^2-10^2))
v=12*12.5/(2.5*22.5)


d=10*v

Answer 2

Answer:

Explanation:

Width = d

Man = V

River = v

In minimum time, he goes perpendicular to the river.

d/V = 10 min------(1)

v x 10 min = 120 m, so v = 12 m /min

In minimum distance, the resultant of the velocities is perpendicular to river

If he is at angle x with the perpendicular

V sinx = v = 12-----(2)

V cosx = d / 12.5-----(3)

Squaring and adding (2) and (3)

2V^2 = 144 + d^2 / 156.25 -----(4)

Putting value of V from (1) in (4),

d^2 /50 = 144 + d^2 /156.25

d^2 = 10500 m

d = 100m

There could be some calculation error, but the method is correct.

Explanation: