Question

Two boats were going downstream with different velocities. When one overtook the other, a plastic ball was dropped from one of the boats. Sometime later, both boats turned back simultaneously and went at the same speeds as before (relative to the river) towards the spot where the ball had been dropped. Which boat will reach the ball first?

• A. The boat which has greater velocity (relative to river).
• B. The boat which has lesser velocity (relative to river).
• C. Both will reach the ball simultaneously.
• D. Cannot be decided unless we know the actual values of the velocities and the time after which they turned around.

Answer 1

The correct option is C Both will reach the ball simultaneously.

From frame of reference of the ball i.e. frame of river, the velocity of both boats is constant for upstream as well as downstream motion.

Let velocity of boat A with respect to river = $V_1=V_{A/w}$
& velocity of boat B with respect to river = $V_2=V_{B/w}$

Let them move for time $t_0$ and then turn back (simultaneousy). Then, in river frame, A has travelled $V_{A/w}\times t_0$
& B has travelled $V_{B/w}\times t_0$
w.r.t the river.

Let them come back to the ball in time $t_1$ and $t_2$ respectively.
$t_1=\frac{V_{A/w}\times t_0}{V_{A/w}}=t_0$
$t_2=\frac{V_{B/w}\times t_0}{V_{B/w}}=t_0$
Hence, both will reach the ball simultaneously.