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## Homework Statement

There is a target at [tex]r_0=x_0i+y_0j+z_0k[/tex] moving with a velocity of [tex]v=v_xi+v_yj+v_zk[/tex] wrt a missle launcher. With what velocity should the missile be launched so as to hit the target, and find the equation of trajectory of the missile.

## The Attempt at a Solution

I did this using relative velocity.

Let the velocity of the missile be [tex]v_m=vm_xi+vm_yj+vm_zk[/tex].

The relative velocity is [tex]v_{rel}=(v_x-vm_x)i+(v_y-vm_y)j+(v_z-vm_z)k[/tex].

The distance between them is [tex]r_0[/tex] and using equations of kinematics, [tex]r_0=v_{rel}t_0[/tex], where [tex]t_0[/tex] is the time to impact.

Now, here at least one of the two should be constant, either the speed of the missile or the time to impact. Assuming the time to impact to be constant, we get [tex]v_{rel}=\frac{r_0}{t_0}[/tex]. Since we know the velocity of the target, we can find the velocity of the missile.

Integrating the velocity of the missile wrt t with limits 0 to [tex]t_0[/tex], we get the trajectory of the missile. Is this correct? Is there some other way to do this?