Projectile Motion Gun Problem: Calculating Elevation Using Equations of Motion

[Arka420]

1. Homework Statement : A gun is fired from a moving platform and the ranges of the shot are observed to be R and S
when the platform is moving forward or backward respectively with
velocity V. Prove that the elevation of the gun is tan(inverse)[g(R - S) ^ 2 / 4V ^ 2(R + S)]
2. Homework Equations : The three equations of motion and the equation for relative velocity.
3. The Attempt at a Solution : I am too confused with the "relative" velocity part. In all probability,we have to obtain a relation between R and S. I have no idea about this problem.

 

[Simon Bridge]

A gun is fired from a moving platform and the ranges of the short are observed to be R and S

... what does "ranges of the short" mean? Do you mean "shot"?
i.e. the projectile goes a distance R when the platform moves forward and S when the platform is moving backwards?

I am too confused with the "relative" velocity part.

You normally do ballistics knowing the velocity of the projectile wrt the ground.
So what is that - bearing in mind the gun is moving.

 

[Arka420]

... what does "ranges of the short" mean? Do you mean "shot"?
i.e. the projectile goes a distance R when the platform moves forward and S when the platform is moving backwards?

Yeah,that is a typo,sorry for that. It would be "shot" only. And your conclusion is correct.

You normally do ballistics knowing the velocity of the projectile wrt the ground.
So what is that - bearing in mind the gun is moving.

With respect to the ground - OK,acceptable,but how do I proceed with the problem exactly? I need to calculate the relative velocity of the projectile wrt ground first,right. DO I assume that the ball is thrown forward(i.e, velocity of projectile is to be added to the velocity of the platform in the first case and subtracted from the velocity of the platform in the second case)?

 

[Orodruin]

I suggest you work backwards. Start by assuming an inclination of the gun and see what velocities (both in x- and y-directions) the bullet has with respect to the ground when being fired in each direction. What path will the bullet follow given the velocity relative to the ground?

 

[Arka420]

I suggest you work backwards. Start by assuming an inclination of the gun and see what velocities (both in x- and y-directions) the bullet has with respect to the ground when being fired in each direction. What path will the bullet follow given the velocity relative to the ground?

Yeah,I think your suggestion is correct. I have done a "time-reversed" problem. (with a ball thrown up a building). So what do you say? Simply find the velocities wrt ground in the two cases and then equate them? Now, the angle θ between the initial velocity and the final velocity is constant. So from there it will be easy to find out the answer. I hope I'm correct.

 

[Simon Bridge]

DO I assume that the ball is thrown forward(i.e, velocity of projectile is to be added to the velocity of the platform in the first case and subtracted from the velocity of the platform in the second case)?

You are asked to consider R to be the range when the velocity of the cart is "forward" wrt the velocity of the projectile.