Question

Car A and Car B travelling on a straight level track points X and Y are 3 km apart on the track. car A passes point X at precisely 10 o’clock travelling to the right at 10 m/s car B passes point Y 2 minutes after car A passes point X travelling to the left at 15 m/s calculate the time and position where car and car b will pass each other?Velocity is constant

Answer 1

First, let's draw a diagram of what is happening

We can solve this by turning this into a system of equations

`d_a=10t`

This equation states where vehicle A is, as it travels 10 m/s per second.

`d_b=3000-15t-120(10)`

We subtract 120(10) from 3000 because that is the distance Car A moves in the two minutes that Car B hasn't moved.

This gives us the 2 equations

da = 10t

& db = 1800 -15t

If we want to find where the distances are the same, we can set both equations to each other

10t = 1800 -15t

1800 = 25t

t = 72 + 120 (2 minutes where vehicle A was already moving) = 192 seconds

We can also find where exactly they crossed each other by solving for distance with one of the two equations.

da = 10(192) = 1920 meters.