Launching a projectile to hit a target moving away from the launch point

[johnsmith122]

Homework Statement

A ball is launched at A with a speed u at an angle ϴ (from the horizontal). Show that if a point P moves so as to keep d/dt(tanα)=constant, then P will "catch" the ball at point B.

Relevant Equations

tanϴ =tanα+tanβ

 

[haruspex]

Your attempt appears to be a random sequence of equations, not directed towards solving the problem.
First, find the x and y location of the projectile as a function of time. Don't substitute a value for g, just leave it as g.
Using those equations, find an equation for the position of P as a function of time.

 

[johnsmith122]

Thanks for the help. I found the x and y location of the projectile to be x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2 but I'm unsure as to how to find an equation for P using this.

 

[haruspex]

Thanks for the help. I found the x and y location of the projectile to be x(t)=ut.cosϴ and y(t)=ut.sinϴ-1/2gt^2 but I'm unsure as to how to find an equation for P using this.

Just a bit of trig. What is the height of (x,y) above P? So what is the horizontal distance from (x,y) to P?