Question #112448

Mark is driving to school when he hits a deer. Immediately after the collision, with the deer on the hood of his car, Mark looks at the speedometer and sees that he has a velocity of 13.0 m/s. The deer has a mass of 70.0 kg and Mark’s car has a mass of 1150 kg. The deer was at rest before the collision. a) How fast was Mark going when he hit the deer? b) Was this collision elastic or inelastic? SHOW ALL OF YOUR WORK!

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Expert's answer

**Explanation**

- Assuming ideal conditions which facilitate the concept -absence of external forces on the system in consideration, the theorem of conservation of linear momentum could be applied to find the initial velocity of the car.
- A collision is known to be elastic if the total initial kinetic energy of the system remains unchanged even after the collision.
- Here the system is defined by the car and the deer

**Notations**

- Refer to the sketch below.

**Calculations**

**1).**

- Applying the above theorem just before and immediate after the collision

"\\qquad \\qquad\n\\begin{aligned}\n\\small m_1u+m_2u_1 &= \\small (m_1+m_2)v\\\\\n\\small 1150kg\\times u + 70kg\\times 0ms^{-1}&= \\small (1150+70)kg\\times 13ms^{-1}\\\\\n\\small u &= \\small \\frac{1220\\times13}{1150}ms^{-1}\\\\\n&=\\small \\bold{13.79 ms^{-1}}\n\\end{aligned}"

**2).**

- Initial kinetic energy of the system (E
_{ki})

"\\qquad \\qquad\n\\begin{aligned}\n\\small E_{ki} &= \\small \\frac{1}{2}\\times1150kg \\times(13.79ms^{-1})^2 \\cdots\\cdots(\\text{Deer has no initial kinetic energy})\\\\\n&= \\small 109344.36J\\\\\n&= \\small \\bold{109.34kJ}\n\\end{aligned}"

- Final kinetic energy of the system(E
_{kf})

"\\qquad \\qquad\n\\begin{aligned}\n\\small E_{kf}&= \\small \\frac{1}{2}\\times(1150+70)kg\\times(13ms^{-1})^2\\\\\n&=\\small 103090J\\\\\n&= \\small \\bold{103.10kJ}\n \n\\end{aligned}"

- Difference between the initial & the final kinetic energies
- "\\qquad\n\\begin{aligned}\n\\small E_{ki}- E_{kf} &= \\small 6.24kJ\\\\\n&=\\small \\bold{ 6240J}\n\\end{aligned}"
- Therefore, this collision is inelastic.

**GOOD LUCK!**

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