A man which travel due north in other to cross a river 5km wide flowing due east at 3km/h. If he can roll at 10km/h in still water. Find either by scale drawing or by calculation (1) the direction in which he must head is boat in order to get to his destination (2) the direction in which he must held his boat in order to get to his destination directly opposite his starting point (3) the velocity of the boat in the river (4) the time taken to cross the river (5) how far from his destination he will be if he ignorantly steared northward.
the diagram
There are errors in your problem that makes it difficult to understand.
X = 3 km/h.
Y = 10 km/h.
Tan A = Y/X = 10/3 = 3.33333.
A = 73.3o N. of E. = 16.7o E. of N.
d1 = 5/Tan73.3 = 1.50 km downstream.
d2 = Sqrt(1.5^2 + 5^2) = 5.22 km to cross.
2. Direction to offset affect of the current: 16.7o W. of N.
d = V*t = 5 km, 10*t = 5, t = 0.5 h.
Vb + 3 = 10i.
Vb = -3 + 10i = 10.44km/h[-73.3o] = 10.44km/h [106.7o] CCW. = 16.7o W. of N.
d = V * t = 5 km.
10t = 5,
t = 0.5h.