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Car A of mass $1500 kg$ travelling at $25 m / s$ collides with another car B of mass $1000 kg$ travelling at $15 m / s$ in the same direction. After collision, the velocity of car a become $20 m / s$ . Calculate the velocity of car B after collision?

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22.5 m / s

20.5 m / s

20 m / s

21 m / s

answer is A.

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Detailed Solution

Car A of mass

1500 kg

travelling at

25 m / s

collides with another car B of mass

1000 kg

travelling at

15 m / s

in the same direction. After collision, the velocity of car a become

20 m / s

. The velocity of car B after collision is

22.5 m / s

.
Given,
Mass of car A,

m_{a} = 1500 kg; m_{b} = 100 kg

, which is the mass of car B.
Velocities:

u_{a} = 25 m / s; v_{a} = 20 m / s

are the velocity of car A before and after collision. respectively.

u_{b} = 20 m / s; v_{b} = ?

represents velocity of car B before and after collision.
By conservation of momentum,

m_{a} u_{a} + m_{b} u_{b} = m_{a} v_{a} + m_{b} v_{b}

\Rightarrow (1500 \times 25) + (1000 \times 15) = (1500 \times 20) + (1000 \times v_{b})

\Rightarrow 37500 + 15000 = 30000 + 1000 v_{b}

\Rightarrow 1000 v_{b} = 22500

{\Rightarrow v}_{b} = 22.5 m / s

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