Time for projectile to cross a line through the origin

[don_anon25]

Projectile Motion -- need urgent help :)

If a projectile is fired from the origin of the coordinate system with an initial velocity v and in a direction making an angle alpha with the horizontal, calculate the time required for the projectile to cross a line passing thorugh the origin and making an angle beta less than alpha with the horizontal.

I know that the position of the projectile is described by
y=y0+v0(sin alpha)*t-4.9t^2.

I let the line be y=ax. I also drew a triangle with Beta as the angle, y=ax as the opposite side, and x as the adjacent side. I'm assuming I want to find y in terms of Beta and then set this equal to y in my projectile motion equation...then solve for t?

Thanks in advance!

 

[Doc Al]

I know that the position of the projectile is described by
y=y0+v0(sin alpha)*t-4.9t^2.

Combine this with the equation for the horizontal position and you can get y as a function of x.

I let the line be y=ax. I also drew a triangle with Beta as the angle, y=ax as the opposite side, and x as the adjacent side. I'm assuming I want to find y in terms of Beta and then set this equal to y in my projectile motion equation...then solve for t?

Write the equation of the straight line. (What is "a" in terms of beta?)

Now you can find the value of x where the two functions intersect. And then plug that into one of the other equations to solve for the time.