Answer to Question #13375 in Mechanics | Relativity for Manas

Question

"A motorship travelling upstreams meets a raft flowing down stream. 45 mins. later the ships stop at a landing stage for 1hr. The ship travels downstreams and overtakes the raft in 1hr. The speed of the water is eqaul to 10km/h. Find the velocity of the current.

Answer 1

Let Vm is the velocity of the current motorship and Vw is the speed of
the
water (so, the velocity of a raft). So, sequentially:
A motorship travelling
upstreams meets a raft flowing down stream at
t0 = 0 s, x0 = 0 m.
t1 = 45
mins = 0.75 hr later the ship stops: x(t1) = x0 + (Vm + Vw) * t1.
After t2 =
1hr: x(t2) = x(t1) + Vw * t2.
The ship travels downstreams and overtakes the
raft in t3 = 1hr.
So, Vm * t3 = x(t2) + Vw * t3
Vm * 1 = 0 + (Vm + 10) *
0.75 + 10 * 1 + 10 * 1
0.25 * Vm = 27.5
Vm = 110 km/h