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# I need help with A 1200 kg car travels at 25.0 m/s and collides head-on in a perfectly inelastic collision with a stationary 2400 kg truck. The kinetic energy lost in the collision is

A 1200 kg car travels at 25.0 m/s and collides head-on in a perfectly inelastic collision with a stationary 2400 kg truck. The kinetic energy lost in the collision is

• Option 1)

330,000 J

• Option 2)

250,000 J.

• Option 3)

125,000 J.

• Option 4)

95,000 J.

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As we discussed in concept

Perfectly Inelastic Collision -

$\fn_jvn v= \frac{m_{1}v_{1}+m_{2}v_{2}}{m_{1}+m_{2}}$

- wherein

Two bodies stick together after the collision ,so there will be a final common velocity (v)

$\fn_jvn m_{1},m_{2}= masses$

$\fn_jvn v_{1}=\: initial \: velocity \: mass\: m_{1}$

$\fn_jvn v_{2}=\: initial \: velocity \: mass\: m_{2}$

From conservation of Linear Momentum

$m_{1}u_{1}+m_{2}u_{2}=(m_{1}+m_{2})v$

$1200\times 25+0 =(1200+2400)v^{'}$

$v^{'}\:=\:\frac{30000}{3600}=8.33$

$\therefore\:lost\:in\:K.E$

$\Delta K=\frac{1}{2}mv^{2}-\frac{1}{2}mv'\:^{2}$

After calculating, we get lost in kinetic energy as 250,000 J

Option 1)

330,000 J

This option is incorrect.

Option 2)

250,000 J.

This option is correct.

Option 3)

125,000 J.

This option is incorrect.

Option 4)

95,000 J.

This option is incorrect.

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