Question

A boy of mass 60 kg running at 3 m/s jumps on to a trolley of mass 140 kg moving with velocity of 1.5 m/s in the same direction. With what velocity will the two moves together?​

Answer 1

Given : A boy of mass 60kg running at 3m/s jumps on to a trolley of mass 140kg moving with velocity of 1.5m/s in the same direction.

To Find : Find the combined velocity of the system ?

_________________________

Solution : Let the combined velocity be x.

$~$

$\underline{\frak{As ~we ~know~ that~:}}$

• $\underset{\blue{\sf Momentum\ Formula}}{\underbrace{\boxed{\frak{\pink{m_{1}u_{1}~+~m_{2}u_{2}~=~m_{1}v_{1}~+~m_{2}v_{2}}}}}}$

$~$

Where,

• ${\sf{Mass~of~boy (m_{1})~=~\bf{60kg}}}$
• ${\sf{Initial~velocity (u_{1})~=~\bf{3m/s}}}$
• ${\sf{Mass~of~trolley (m_{2})~=~\bf{140kg}}}$
• ${\sf{Initial~velocity (u_{2})~=~\bf{1.5m/s}}}$

$~$

◗Both are moving in same direction and we have to calculate the combined velocity Since, the combined mass of the system is 60 + 140 = 200kg.

$~$

• ${\sf{m_{1}u_{1}~+~m_{2}u_{2}~=~m_{1}v_{1}~+~m_{2}v_{2}}}$

$~$

$\pmb{\sf{\underline{According ~to ~the ~Given ~Question~:}}}$

$~$

$\qquad{\sf:\implies{m_{1}u_{1}~+~m_{2}u_{2}~=~m_{1}v_{1}~+~m_{2}v_{2}}}$

$\qquad{\sf:\implies{\bigg(60~×~3\bigg)~+~\bigg(140~×~1.5\bigg)~=~200~×~v}}$

$\qquad{\sf:\implies{180~+~210~=~200~×~v}}$

$\qquad{\sf:\implies{390~=~200~×~v}}$

$\qquad{\sf:\implies{v~=~\cancel\dfrac{390}{200}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{v~=~1.95~m/s}}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{The ~combined ~velocity~ of~ the ~system ~is~\bf{\underline{\pmb{1.95~m/s}}}}}$

Answer 2

Answer:

This is your answer hope it's help u

Hii gud morning how are you