Kinematics and vectors -- A heavy box is being pulled using two tractors....

[Dominator007]

Homework Statement

A heavy box is being pulled using two tractors. Oneof these has velocity v1, the other v2, the angle between velocities is α. What is the velocity of the box, if we assume that the ropes are parallel to velocity vectors?

Relevant Equations

V1+V2=√v1^2+v2^2+2v1v2cos(alpha)

I solved it using parallelogram law if vector addition but didn't got the correct answer.why?
Is their any other way to add velocity vectors.
How to do this problem

 

[TSny]

Welcome to PF!

The velocity of the box does not equal the vector sum of the tractor velocities, in general. For example, take the simple case where the angle $\alpha$ is zero and $\vec V_1 = \vec V_2$. Then the box's velocity would be $\vec V_{box} = \vec V_1 = \vec V_2$, not $\vec V_{box} = \vec V_1+ \vec V_2$.

The solution of the general problem is based on the idea that the ropes cannot stretch or go slack. If $\theta_1$ is the angle between $\vec V_{box}$ and $\vec V_1$, what must be the relation between $\vec V_{box}$ and $\vec V_1$ in order that the rope for tractor 1 doesn't stretch or become slack?