Calculate

Calculate the resulting speed of both vehicles after the accident of a car with a mass of m₁ = 1.5 tons traveling at a speed of 100 km/h and a truck with a mass of m₂ = 40 tons traveling at a speed of 90 km/h, if it is a head-on accident.

Calculate the overload acting on the passenger car if the speed change occurred at t= 50 milliseconds.

Correct answer:

v =  -83.1325 km/h
g =  103.7108 g

Step-by-step explanation:

$$\begin{gathered} m_1=1.5\text{t}\to \text{kg}=1.5\cdot 1000\text{kg}=1500\text{kg} \\ {m}_2=40\text{t}\to \text{kg}=40\cdot 1000\text{kg}=40000\text{kg} \\ {v}_1=100\text{km/h}\to \text{m/s}=100:3.6\text{m/s}=27.77778\text{m/s} \\ {v}_2=-90\text{km/h}\to \text{m/s}=-90:3.6\text{m/s}=-25\text{m/s} \\ {h}_1+h_2=0 \\ {m}_1\cdot v_1+m_2\cdot v_2=(m_1+m_2)v \\ {v}_3=\frac{m_1\cdot v_1+m_2\cdot v_2}{m_1+m_2}=\frac{1500\cdot \frac{250}{9}+40000\cdot (-25)}{1500+40000}=-\frac{5750}{249}\doteq -23.0924\text{m/h} \\ v=v_3\to \text{km/h}=v_3\cdot 3.6\text{km/h}=(-23.0924)\cdot 3.6\text{km/h}=-83.133\text{km/h}=-\frac{6900}{83}\text{km/h}=-83.1325\text{km/h} \end{gathered}$$

$$\begin{gathered} g_0=9.81{\text{m/s}}^2 \\ t=50\cdot 10^{-3}=0.05\text{s} \\ a=(v_1-v_3)/t=(\frac{250}{9}-\frac{-5750}{249})/\frac{1}{20}\doteq 1017.4029{\text{m/s}}^2 \\ g=a/g_0=1017.4029/9.81=103.7108\text{g} \end{gathered}$$

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