Answer:
The velocity of one of the trains is 15 m/s
The velocity of the other train 5 m/s
Explanation:
The given parameters of the two trains and the motion of the trains are;
The length of each train, l = 100 m
The time it takes one train to overtake the other, Δt₁ = 20 s
The time it takes the one train to cross the other, Δt₂ = 10 s
Let 'v₁' represent the velocity of one of the trains, and let 'v₂' represent the velocity of the other train, we have;
When one train overtakes the other, the trains are moving in the same direction and the relative velocity of the overtaking train, v = v₁ - v₂
The distance the train travels when overtaking or crossing, d = 2 × l
∴ d = 2 × 100 m = 200 m
d = 200 m
Therefore, we get;
v = v₁ - v₂ = d/Δt₁ = (200 m)/(20 s) = 10 m/s
∴ v₁ - v₂ = 10 m/s [tex]{}[/tex] Equation (1)
When one train crosses the other train, the trains are moving in opposite directions on the different tracks, therefore, we have;
For the overtaking trains, v = v₁ + v₂ = d/Δt₂ = (200 m)/(10 s) = 20 m/s
∴ v₁ + v₂ = 20 m/s [tex]{}[/tex] Equation (2)
Adding equation (1) to equation (2) gives;
v₁ - v₂ + v₁ + v₂ = 2·v₁ = 10 m/s + 20 m/s = 30 m/s
∴ v₁ = 30 m/s/2 = 15 m/s
The velocity of one of the trains, v₁ = 15 m/s
From equation (2), we have;
v₁ + v₂ = 20 m/s
v₂ = 20 m/s - v₁
∴ v₂ = 20m/s - 15 m/s = 5 m/s
The velocity of the other train, v₂ = 5 m/s.