2 Projectiles are fired simultaneously

[Om Swostik]

Homework Statement

2 projectiles are fired simultaneously from ground level with same initial speed (u).Both cover same horizontal distance of 160m on reaching the ground level .One of them reaches 6 sec prior to the other.Only gravitational acceleration g=10m/s squared governs the motion of both the projectile.Calculate u.[/B]

Homework Equations

Range(horizontal distance)=u squared sin 2×theta/g= Ux cos theta ×time
Time=2u sin theta/g
Where ,
U is initial velocity
Theta is the angle of projection
and T is the time taken by the projectile to reach ground level.
Note:vector u has 2 components which are Ux=u cos theta and Uy=u sin theta

The Attempt at a Solution

 

[haruspex]

Homework Statement

2 projectiles are fired simultaneously from ground level with same initial speed (u).Both cover same horizontal distance of 160m on reaching the ground level .One of them reaches 6 sec prior to the other.Only gravitational acceleration g=10m/s squared governs the motion of both the projectile.Calculate u.[/B]

Homework Equations

Range(horizontal distance)=u squared sin 2×theta/g= Ux cos theta ×time
Time=2u sin theta/g
Where ,
U is initial velocity
Theta is the angle of projection
and T is the time taken by the projectile to reach ground level.
Note:vector u has 2 components which are Ux=u cos theta and Uy=u sin theta

The Attempt at a Solution

An attempt is required. Forum rules.

 

[Om Swostik]

THE ATTEMPT AT A SOLUTION:
I took the angle of projection of 1st projectile as theta and the angle of the 2nd one as 90 - theta (as there can be two angles of projection for the same range).
I equated the range and the time ,that is
T=t+6.As I have really limited knowledge of trigonometry, the resulting equation which I arrived at couldn't be solved by me.

 

[haruspex]

THE ATTEMPT AT A SOLUTION:
I took the angle of projection of 1st projectile as theta and the angle of the 2nd one as 90 - theta (as there can be two angles of projection for the same range).
I equated the range and the time ,that is
T=t+6.As I have really limited knowledge of trigonometry, the resulting equation which I arrived at couldn't be solved by me.

Please post the equation. It might save time to post your working too, in case you have a mistake somewhere.