Final answer:
The two trains will take approximately 21.58 seconds to completely pass one another.
Step-by-step explanation:
In order to determine the time it will take for the two trains to completely pass one another, we need to find the relative velocity between them. We can do this by subtracting the velocity of the second train from the velocity of the first train.
First, we need to convert the velocity of the first train from km/h to m/s. Since 1 km = 1000 m and 1 hour = 3600 s, we multiply the velocity of the first train (52 km/h) by (1000 m/1 km) and divide by (3600 s/1 hour) to get 14.44 m/s.
Next, we subtract the velocity of the second train (20 m/s) from the velocity of the first train (14.44 m/s) to get the relative velocity. The relative velocity is 14.44 m/s - 20 m/s = -5.56 m/s. Since the relative velocity is negative, it means the trains are moving towards each other.
To find the time it will take for the trains to completely pass one another, we can use the formula time = distance/velocity. The distance is given as 120 m and the velocity is the relative velocity of -5.56 m/s. Plugging in these values, we get time = 120 m/(-5.56 m/s) = -21.58 s. Since it doesn't make sense to have a negative time, we can take the absolute value to get the positive time.
Therefore, it will take approximately 21.58 seconds for the two trains to completely pass one another.