Answer
$8.59 \ km/h$
Work Step by Step
We know the following equation:
$x = v_0t + \frac{1}{2}at^2$
Thus, we find:
$x_{20}+v_{20}t= v_{10}t + \frac{1}{2}at^2$
$0= v_{10}t + \frac{1}{2}at^2-x_{20}-v_{20}t$
Solving for t by applying the quadratic formula, we plug in the known values to find:
$t = \frac{(23.61-16.67)\pm\sqrt{(23.61-16.67)^2-4(\frac{-1}{2})(4.2)(10)}}{-4.2\times 2 \times \frac{1}{2}}=1.085 \ seconds$
Thus, we find the velocity of the second car:
$v = v_1 - 60\ km/h$
$v = (23.61-(4.2)(1.085))(3.6 \frac{km/h}{m/s}) - 60\ km/h=8.59 \ km/h$
