Given,
The velocity of the objects, v₁=50.0 m/s and v₂=-25.0 m/s
The initial positions of the objects, x₁_₀=0.00 m and x₂_₀=500 m
The relative velocity of the objects is given by,
On substituting the known values,
The total distance between the objects is,
(a)
As the two objects are traveling towards each other in a straight line, they will intercept.
The time it takes for the objects to intercept is given by,
On substituting the know values,
As t is the time it takes for the objects to intercept, the distance covered by the objects in this time will give us the position x_f where these two objects intercept.
As object 1 starts from the origin, the distance traveled by this object is equal to x_f
The distance traveled by object 1 in that time is,
On substituting the known values,
Thus the objects will intercept at the point x_f=333.5 m from the origin.
(b)
As calculated in part a, the time it takes for the objects to intercept is t=6.67 s