What is a Vector?
Understanding relative velocity
Relative velocity concepts:
Velocity of the truck w.r.t ground,
V_t = + 80 km/hr (forward)
Velocity of the man w.r.t truck,
V_mt = - 80 km/hr (backward)
V_mt = V_m - V_t
Velocity of the man w.r.t ground,
V_m = V_mt + V_t
= - 80 + 80
= 0 km/ hr
From https://www.surendranath.org/
Relative Displacement, Relative Velocity, Relative Acceleration Concepts.
How to calculate from the given data whether the trucks will collide or not?
During collision, the relative displacement of A (Green) w.r.t. B (Yellow) is Zero.
So if we use
$S_{AB} = S_{oAB} + u_{AB}t + \frac{1}{2} a_{AB}t^2$
$S_{A}-S_{B}=\left(S_{oA}-S_{oB}\right)+\left(u_A-u_B \right) t + \frac{1}{2} \, \left(a_A-a_B\right) t^2 $
From the quadratic equation so obtained if we try to solve for time t, if the time is real the collision is also real, so the trucks will collide, if the time is unreal or imaginary, then the collision is also unreal or imaginary, so the trucks will not collide.
Discriminant term inside the square root should be checked.
$ b^2-4ac < 0 $
$\left(u_A - u_B\right)^2 - 4 .\frac{1}{2}.\left(a_A-a_B\right) \left(S_{oA}-S_{oB}\right) < 0 $
is the condition to avoid crash.
In other words the initial relative speed has to be lower,
the relative acceleration has to be lower and
relative displacement has to be higher in magnitude.
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