Answer:
The angle at which the boat must head is
Solution:
As per the solution:
Distance between the parallel banks, d = 40 m
The maximum speed of water, v' = 3 m/s
constant speed, u' = 5 m/s
Also,
The speed of water of the river at a distance of 'x' units from the west bank is given as a sine function:
(2)
Now, to determine the angel at which the boat must head:
The velocity of the engine of the boat:
v =
v =
The abscissa of the boat at time t:
v =
Now, from above and eqn(1) , we can write:
Now, boat's velocity at time t:
v =
In order to obtain the position of the boat, we integrate both the sides, we get:
r = + C (3)
Now, at r = 0:
0 = + C
C =
Now, from eqn (3)
r = (4)
the baot will reach the point at y = 0 and x = 40
Now,
40 =
Substituting the above value of 't' in eqn (4):
r =
We get: