Question

Hello sir
My question is this: If two cars which are exactly the samme hit each other in a head to head position, one of them has a velocity of 50km/h and the other one has a velocity of 5km/h, What would be the impact of the crash for each car ? and what would be the velocity of each car after the crash ?
Thank you so much

Answer 1

Answer on Question #61054, Physics / Classical Mechanics

Let us denote initial velocity of first and second vehicle $v_{1}, v_{2}$ , and choose $x$ direction so that $v_{1} = 50\frac{km}{h}$ , $v_{2} = -5\frac{km}{h}$ . Let the velocities after impact be $v_{1}', v_{2}'$ .

Using law of conservation of momentum, obtain $m v_{1} + m v_{2} = m v_{1}^{\prime} + m v_{2}^{\prime}$ , from where $v_{1}^{\prime} = 45 - v_{2}^{\prime}$ . Using law of conservation of energy, obtain $\frac{m v_{1}^{2}}{2} + \frac{m v_{2}^{2}}{2} = \frac{m v_{1}^{\prime 2}}{2} + \frac{m v_{2}^{\prime 2}}{2}$ , from where $v_{1}^{2} + v_{2}^{2} = v_{1}^{\prime 2} + v_{2}^{\prime 2}$ . Substituting $v_{1}^{\prime} = 45 - v_{2}^{\prime}$ and numerical values of $v_{1}, v_{2}$ into last expression, obtain $v_{2}^{\prime 2} - 45 v_{2}^{\prime} - 250 = 0$ . Solving quadratic equation, obtain $v_{2}^{\prime} = 50$ , and $v_{1}^{\prime} = 45 - v_{2}^{\prime} = -5$ , hence the first car will be moving back with velocity $5\frac{km}{h}$ and the second car will be moving forward with velocity $50\frac{km}{h}$ .

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