Question

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 690.0 kg and was traveling eastward. Car B weighs 520.0 kg and was traveling westward at 74.0 km/h. The cars locked bumpers and slid eastward with their wheels locked for 6.00 m before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750. 1) How fast (in kilometer per hour) was car A traveling just before the collision? (Express your answer to three significant figures.)

Answer 1

Answer:

115 km/h

Explanation:

$m_1$ = Mass of car A = 690 kg

$m_2$ = Mass of car B = 520 kg

g = Acceleration due to gravity = 9.81 m/s²

a = Acceleration

u = Initial velocity

v = Final velocity

$a=\mu g\\\Rightarrow a=0.75\times 9.81\\\Rightarrow a=7.3575\ m/s^2$

$v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 7.3575\times 6+0^2}\\\Rightarrow v=9.396\ m/s$

$m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow u_1=\frac{(m_1 + m_2)v-m_2u_2}{m_1}\\\Rightarrow u_1=\frac{(690+520)9.396-520\times -\frac{74}{3.6}}{690}\\\Rightarrow u_1=31.96\ m/s$

Converting to km/h

$31.96\times 3.6=115.056\ km/h$

Initial velocity of car A = 115 km/h