Question

A trolley containing water has total mass of $4000\text{kg}$ and is moving at a speed of $40\text{m/s}$. Now water starts coming out of a hole from the bottom of the trolley at the rate of $8\text{kg/s}$. Speed of trolley after $50\text{s}$ is

• A. $44.4\text{m/s}$
• B. $40\text{m/s}$
• C. $64\text{m/s}$
• D. $54.44\text{m/s}$

Answer 1

The correct option is A $44.4\text{m/s}$

Given that,
Initial mass of water $\left(m_1\right)=4000\text{kg}$
Initial velocity of trolley $v_1=40\text{m/s}$
Rate of water coming out from the hole $\left(m_r\right)=8\text{kgs}$
Total mass of water flown out after $\left(m_3\right)50\text{s}=8\text{kgs}\times 50\text{s}$
$\Rightarrow m_3=400\text{kg}$
The direction of water coming out from the trolley is vertically downward.
The momentum of the system in horizontal direction will not change.
Initial momentum in horizontal direction = Final momentum in horizontal direction.
$m_1{v}_1=(m_1-m_3)v_2$
$4000\times 40=(4000-400)v_2$ ($v_2$= velocity of trolley after $50\text{s}$ )
$v_2=44.44m/s$