Question

Two boats $A$ and $B$ are moving along perpendicular paths in a still lake at night. At $t=0$, the boats are $300\text{m}$ apart. If boat $A$ moves with a speed of $3\text{m/s}$ and boat $B$ moves with a speed of $4\text{m/s}$ in a direction such that they can collide after sometime, then the boats will collide after

• A. $80\text{s}$
• B. $40\text{s}$
• C. $60\text{s}$
• D. $20\text{s}$

Answer 1

The correct option is C $60\text{s}$

Let us suppose the boats collides after time $t\text{sec}$, then the distance moved by boat $A$ will be $3t$ and by boat $B$ will be $4t$.
From the data given in the question, let us draw a figure as shown below,

From the figure, we can say that,
$(3t{)}^2+(4t{)}^2=(300{)}^2$
On solving this, we get,
$t=60\text{s}$
Thus, option (c) is the correct answer.