Projectile motion problem (moving ships firing a projectile)

[Istiak]

Homework Statement

Two ships are traveling parallel to each other in opposite directions with speeds v_1 and v_2 One ship fires on the other. At what angle \phi (with respect to the direction of the firing ship) should the gun be aimed at the target ship in order to make a if the shot is fired at the instant when both vessels are on the straight line perpendicular to their course? The shell velocity v_0 is assumed constant.

Relevant Equations

v=u+at

Question :

Solution attempt :

 

[haruspex]

Please do not post images of working. That is for diagrams and textbook extracts.
Type the algebra in, define the variables, and explain the basis of each starting equation.

 

[Delta2]

How can we interpret the statement "if the shot is fired at the instant when both vessels are on the straight line perpendicular to their course". I interpret it as follows: The ships are in two parallel lines which have distance $d$ and the shot is fired when the distance between the ships equals $d$. @haruspex what do you think about this?

 

[haruspex]

How can we interpret the statement "if the shot is fired at the instant when both vessels are on the straight line perpendicular to their course". I interpret it as follows: The ships are in two parallel lines which have distance $d$ and the shot is fired when the distance between the ships equals $d$. @haruspex what do you think about this?

Yes. The original would have been fine had it said:
"if the shot is fired at the instant when the vessels are on the same straight line perpendicular to their course"

 

[Delta2]

Yes. The original would have been fine had it said:
"if the shot is fired at the instant when the vessels are on the same straight line perpendicular to their course"

well, now that we agreed at the interpretation, I think that in order to solve this problem we need to determine two angles the angle of $\vec{v_0}$ with the z-axis (gravity axis) and the angle of $\vec{v_0}$ with one of the parallel lines.
Edit something tells me that the problem wants only the second angle, the first angle is considered to be 90 (or zero) that is shot parallel to horizontal plane.

 

[haruspex]

well, now that we agreed at the interpretation, I think that in order to solve this problem we need to determine two angles the angle of $\vec{v_0}$ with the z-axis (gravity axis) and the angle of $\vec{v_0}$ with one of the parallel lines.
Edit something tells me that the problem wants only the second angle, the first angle is considered to be 90 (or zero) that is shot parallel to horizontal plane.

Since we are not given any distances, we can't consider the vertical motion. We can either suppose that is negligible or interpret the shell velocity as just its horizontal component. Indeed, those are the only ways for that velocity to be considered constant.

 

[Delta2]

To @Istiakshovon : I think you have misunderstood the statement of the problem and your work is towards solving a different problem. The situation in this problem is like this picture shows

i misnamed the angle as \theta, that is the \phi angle of the problem statement actually.