Question

A truck is moving on a frictionless surface with a uniform velocity of $10m{s}^{-1}$. A leak occurs in the water tank of the truck at the rate of $2kg{s}^{-1}$. What is the speed of the truck after $50s$, if the mass of the truck is $100kg$ and the mass of water in the truck initially was $100kg$?

• A. $20m{s}^{-1}$
• B. $10m{s}^{-1}$
• C. $15m{s}^{-1}$
• D. None of the above

Answer 1

The correct option is A

$20m{s}^{-1}$

Step 1. Given Data:

The combined mass of the system $M=100+100$$=200kg$

The velocity of the truck, $v=10m{s}^{-1}$

The rate at which the water leaks, $r=2kg{s}^{-1}$

Step 2. Find the velocity:

Water lost in $50s$ is given by $Q=2\times 50$$=100kg$

The final mass of the system is $M_f=M-Q$

$=200-100$

$=100kg$

Assume the final velocity of the truck as $v_f$

Now, from the conservation of linear momentum we have

$Mv=M_f{v}_f$

$200\times 10=100\times v_f$

$\Rightarrow$ $v_f=20m{s}^{-1}$

Hence, option (A) is correct.