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

44.4 m/s

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40 m/s

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64 m/s

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54.44 m/s

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Solution

The correct option is A $44.4 m/s$
Given that,
Initial mass of water $(m_{1}) = 4000 kg$
Initial velocity of trolley $v_{1} = 40 m/s$
Rate of water coming out from the hole $(mr)=8 kg\s$
Total mass of water flown out after $(m3) 50 s=8 kg\s×50 s$
$\Rightarrow m_{3} = 400 kg$
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 $50 s$ )
$v_{2} = 44.44 m / s$

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

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