Question

A man on a wharf 12 mt above the water level pulls in a rope to which a boat is attached at the rate of $1$ mt per second. At what rate is the boat approaching the shore, when there is still $13$ mt rope out ?

• A. $2.6$ m/sec
• B. $2$ m/sec
• C. $5$ m/sec
• D. $6.5$ m/sec

Answer 1

The correct option is A $2.6$ m/sec

We can observe a Right angled Triangle in this case, in which rope is the Hypotenuse and Horizontal distance is the base and Height = $12m$

Now, Since, the height is constant

we can write the relation between sides as

${12}^2+x^2=y^2$

where $x\to baselengthy\to ropelength$

Differentiating above equation with respect to t and putting value of x and y at $y=13\to x=5$

$2x\frac{dx}{dt}=2y\frac{dy}{dt}\Rightarrow \frac{dx}{dt}=\frac{y}{x}\frac{dy}{dt}\Rightarrow v=\frac{13}{5}\ast 1=\frac{13}{5}=2.6m/s$