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A car of mass 580 kg collides with the rear of a stationary van of mass 1200 kg - AQA - A-Level Physics - Question 22 - 2017 - Paper 1

Question 22

A car of mass 580 kg collides with the rear of a stationary van of mass 1200 kg. Following the collision, the van moves with a velocity of 6.20 m s⁻¹ and the car re... show full transcript

Worked Solution & Example Answer:A car of mass 580 kg collides with the rear of a stationary van of mass 1200 kg - AQA - A-Level Physics - Question 22 - 2017 - Paper 1

Step 1

Using Conservation of Momentum

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Answer

In an inelastic collision, momentum is conserved. The initial momentum before the collision can be expressed as:

$ext{Initial Momentum} = m_{car} imes v_{car} + m_{van} imes 0$

The final momentum after the collision will be:

$ext{Final Momentum} = m_{car} imes (-1.60) + m_{van} imes 6.20$

Given:

Mass of car, $m_{car} = 580 ext{ kg}$
Mass of van, $m_{van} = 1200 ext{ kg}$

Setting initial momentum equal to final momentum:

$580 imes v_{car} = 580 imes (-1.60) + 1200 imes 6.20$

Step 2

Solving for the Initial Speed of the Car

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Answer

Substituting the known values into the equation:

Calculate the final momentum:

$580 imes (-1.60) + 1200 imes 6.20 = -928 + 7440 = 6512 ext{ kg m s}^{-1}$

Therefore, the equation becomes:

$580 imes v_{car} = 6512$

Solving for $v_{car}$ :

$v_{car} = \frac{6512}{580} ≈ 11.22 ext{ m s}^{-1}$

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