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You should rather walk perpendicular to the line connecting you and the car, and not perpendicular to the street.

The task is to minimize the ratio a/c since a and c are the paths that you and the car respectively traverses before you meet. And if that ratio is minimized we have found the path that allows the lowest possible speed for you.

So we want to find the minimum of a/c when we vary the angle v. Side a and c varies with v. Side b is constant, and angle u is constant.

The Law of sines tells us that sin(v)/c = sin(u)/a. So a/c = sin(u)/sin(v). Sin(u) is constant, so a/c is minimized when sin(v) is maximized, which happens when v=90 degrees, i.e. you walk perpendicular to the line b connecting you and the car.