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A 1,571 kilogram car travelling at 129 kilometers per hour is driving down a highway. The driver suddenly realizes a large animal is standing stationary on the highway in the way of the car. The driver manages to release their foot off the accelerator peddle, but does not have time to hit the brake peddle. The car strikes the animal which gets stuck to the car hood. Immediately after the collision the car slows to 59 kilometers per hour. Given this information, accident investigators are able to determine the mass of the animal as what

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Answer:

[tex]1863.9\ \text{kg}[/tex]

Explanation:

[tex]m_1[/tex] = Mass of car = 1571 kg

[tex]u_1[/tex] = Initial velocity of car = 129 km/h

[tex]u_2[/tex] = Initial velocity of the animal = 0

[tex]v[/tex] = Velocity of combined mass = 59 km/h

[tex]m_2[/tex] = Mass of the animal

As the momentum of the system is conserved we have

[tex]m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow \dfrac{m_1u_1+m_2u_2}{v}-m_1=m_2\\\Rightarrow m_2=\dfrac{1571\times 129+0}{59}-1571\\\Rightarrow m_2=1863.9\ \text{kg}[/tex]

The mass of the animal is [tex]1863.9\ \text{kg}[/tex].

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