The driver of a passenger car starts overtaking the trailer at a speed of 90 km / h at the time when the distance

The driver of a passenger car starts overtaking the trailer at a speed of 90 km / h at the time when the distance between cars is s1 = 20 m, and moves (rebuilds) into the previous lane when the distance between cars becomes s2 = 15 m. Determine the time it took for the driver to overtake a trailer traveling at 72 km / h. The length of a car is 4 m, of a trailer – 16 m.

Vа = 90 km / h = 25 m / s.

S1 = 20 m.

S2 = 15 m.

Vtr = 72 km / h = 20 m / s.

Lа = 4 m.

Ltr = 16 m.

t -?

We will consider the movement of a car relative to the trailer.

With uniform rectilinear movement, to find the overtaking time t, the distance S, which the passenger car has traveled, must be divided by the speed V: t = S / V.

The car must first catch up with the trailer, go through the path S1. Overtaking begins when the passenger car cab is flush with the rear of the trailer and ends when the rear of the car is flush with the trailer. Therefore, directly during overtaking, the car travels the distance Lа + Lтр.

S = S1 + La + Ltr + S2.

Since cars are moving in one direction, the speed of a passenger car relative to a truck will be the difference: V = Vа – Vtr.

t = (S1 + Lа + Ltr + S2) / (Vа – Vtr).

t = (20 m + 4 m + 16 m + 15 m) / (25 m / s – 20 m / s) = 11 s.

Answer: overtaking the trailer lasted t = 11 s.