# two objects, and where they meet

**1. The problem statement, all variables and given/known data**

A worker with a mass of M

_{w}is pulling on a mass-less rope that is attached to a box with a mass of m

_{b}on a friction-less surface. The worker pulls with a constant force starting at rest. The Worker is at x = 0, and the box is at x

_{b}Find the position at which they meet in terms given.

**2. Relevant equations**

x = x_{i} + v_{i} * t + 1/2 a * t^{2}

F = m * a

**3. The attempt at a solution**

Using newton’s laws I know that the force on each object is equal, so

F_{w} = F_{b}

x_{w f} = x_{w i} + v_{w i}* t + 1/2 a * t^{2}

thus for the worker’s side of the equation

x_{w f} = 1/2 a * t^{2}

and the box moves

x_{b f} = x_{b i} + v_{b i}* t – 1/2 a * t^{2}

thus

x_{b f} = x_{b i} – 1/2 a * t^{2}

since they meet x_{b f} is equal to x_{w f}

thus

1/2 a * t^{2} = x_{b i} – 1/2 a * t^{2}

x_{b i} = 1/2 a_{w} * t^{2} + 1/2 a_{b} * t^{2}

2 x_{b i} = (a_{w} + a_{b}) * t^{2}

t = √( ( 2 * x_{b i}) / a_{w} + a_{b})

then taking what I have just solved for time, and plugging that back into the basic kinematic equation to find the distance I get jibberish. So I’m not sure where to go from here.

x_{meet} = x_{initial} + 1/2 a_{worker} * ( ( 2 * x_{b i}) / a_{w} + a_{b})

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