Which Regions Can This Cannon Reach with Its Projectile?

[roborangers]

Homework Statement

A cannon is situated in the origin of coordinate axes
and can give initial velocity v0 to a projectile, the shooting direction can be chosen at will. What is the region of space R
that the projectile can reach?

Relevant Equations

but when i checked the solution i say that kalda added y+gx^2/2v_0^2 but i dont understand why

what i tried to do is to write y=v_0tsin alpha - 1/2gt^2 and x=v_0 cos alpha tand that t=x/v_0 cos alphai plug t in the formula for y and get that y= x tan alpha - gx^2/v_0^2 (tan^2 alpha -1)since jaan klada said there should be a quadratic equation (because its a parabola) i thought that gx^2/v_0^2 tan^2 alpha is a, -x tan alpha is b and gx^2/2v_0 is c and got another formula

 

[PeroK]

Homework Statement: A cannon is situated in the origin of coordinate axes
and can give initial velocity v0 to a projectile, the shooting direction can be chosen at will. What is the region of space R
that the projectile can reach?
Relevant Equations: but when i checked the solution i say that kalda added y+gx^2/2v_0^2 but i dont understand why

what i tried to do is to write y=v_0tsin alpha - 1/2gt^2 and x=v_0 cos alpha tand that t=x/v_0 cos alphai plug t in the formula for y and get that y= x tan alpha - gx^2/v_0^2 (tan^2 alpha -1)since jaan klada said there should be a quadratic equation (because its a parabola) i thought that gx^2/v_0^2 tan^2 alpha is a, -x tan alpha is b and gx^2/2v_0 is c and got another formula

This is not easy to read. Punctuation and spacing are important.

 

[roborangers]

This is not easy to read. Punctuation and spacing are important.

yes you are righ but i got it

 

[kuruman]

The correct equation for the projectile trajectory is $$y=x\tan\alpha-\frac{gx^2}{2g}(1+\tan^2\alpha).$$The general equation for the quadratic equation is $$ax^2+bx+c=0$$.What exactly is your question? When you say "What is the region of space R that the projectile can reach?" do you mean in the horizontal direction only or in two dimensional space?

I don't know who Jaan Kalda is, but I think that you should include the whole answer that he provided not just the term that he added.

 

[roborangers]

yes exactly i got that y is v_0^2/2g - gx^2/2v_0^2