Question

Question one I need an explanation Pls. Only part a and b.

Answer 1

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,

`v=v_1-v_2`

On substituting the known values,

`\begin{gathered} v=50.0-(-25.0) \\ =75.0\text{ m/s} \end{gathered}`

The total distance between the objects is,

`\begin{gathered} d=x_(10)+x_(20) \\ =0+500 \\ =500\text{ m} \end{gathered}`

(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,

`t=(d)/(v)`

On substituting the know values,

`\begin{gathered} t=(500)/(75) \\ =6.67\text{ s} \end{gathered}`

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,

`x_f=d_1=v_1t`

On substituting the known values,

`\begin{gathered} x_f_{}=50*6.67 \\ =333.5m\text{ } \end{gathered}`

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