Calculating the New Angle of Inclination for a Projectile Launcher

[adivit]

In the experimental setup similar to the one shown during the class demonstration, the small ball is launched from the
corner of inclined plane. When the inclination of the plane is 70deg the maximum range of the projectile is 50cm. Later
the inclination of the plane changes to new unknown angle and the same projectile launcher is oriented at 30 deg to the
horizontal line. The ball lands 1m away from the launcher. Find the new angle of inclination.
How do i do it? i tried everything , i tried finding initial speed of the projectile but i get 2 unknows, etc. any suggestion on what to do?

 

[Simon Bridge]

Welcome to PF;
1. draw a picture of what is happening.

I take it the "range" is measured along the slope and not horizontally?You work out the equations for the motion in general - then put numbers in.
Lets have the plane inclined at angle $\phi$ to the horizontal and the launcher shoots at angle $\theta$ to the horizontal.

The muzzle-speed of the projectile is the same for both experiments.

In experiment 1 you are given the maximum range of the projectile... what angle of launcher gives the maximum range? (Does the slope of the plane affect this?)

In experiment 2 you are given the range for a specific angle.

2. You can work out an equation for x(t) and y(t) for the projectile, and y_p(x) - the equation of height of the plane in the x direction.

3. From there you can find the time of flight (time it takes for the x-y trajetory of the projectile to intersect the line of the plane) and a slew of other equations. At some point you'll have as many equations as you have unknowns... then you can solve it.