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What is the velocity (in m/s) of a 950 kg car initially moving at 26.5 m/s, just after it hits a 135 kg deer initially running at 12.5 m/s in the same direction?

Answer :

To solve this problem, we need to use the law of conservation of momentum. This law states that in an isolated system (no external forces), the total momentum before a collision is equal to the total momentum after the collision.

Here are the steps to solve the problem:


  1. Identify the masses and velocities before the collision:


    • Mass of the car, [tex]m_1 = 950 \; \text{kg}[/tex]

    • Initial velocity of the car, [tex]v_1 = 26.5 \; \text{m/s}[/tex]

    • Mass of the deer, [tex]m_2 = 135 \; \text{kg}[/tex]

    • Initial velocity of the deer, [tex]v_2 = 12.5 \; \text{m/s}[/tex]



  2. Calculate the total momentum before the collision:


    • Total momentum [tex]p_{\text{initial}} = m_1 \times v_1 + m_2 \times v_2[/tex]

    • [tex]p_{\text{initial}} = 950 \times 26.5 + 135 \times 12.5[/tex]

    • [tex]p_{\text{initial}} = 25175 + 1687.5[/tex]

    • [tex]p_{\text{initial}} = 26862.5 \; \text{kg m/s}[/tex]



  3. Using conservation of momentum, set the initial momentum equal to the final momentum:


    • Let [tex]v_f[/tex] be the final velocity of the car and deer together

    • Total mass after collision = [tex]m_1 + m_2 = 950 + 135 = 1085 \; \text{kg}[/tex]

    • [tex]p_{\text{initial}} = p_{\text{final}}[/tex]

    • [tex]26862.5 = 1085 \times v_f[/tex]



  4. Solve for the final velocity [tex]v_f[/tex]:


    • [tex]v_f = \frac{26862.5}{1085}[/tex]

    • [tex]v_f \approx 24.75 \; \text{m/s}[/tex]




Therefore, the velocity of the car just after it hits the deer is approximately [tex]24.75 \; \text{m/s}[/tex]. This result assumes no external forces interfere and the system is isolated.

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Rewritten by : Barada