Finding the angle of projection and its speed in 2D Kinetics

[dahano]

Homework Statement

: The trajectory of a projectile in a vertical plane is y = √3 x - (1/5)x², where x and y are respectively horizontal and vertical distances of the projectile from the point of projection. Find the angle of projection and speed of projection.[/B]

Homework Equations

: 2-Dimensional Equations and maybe calculus.[/B]

The Attempt at a Solution

: Honestly, I can't even understand that how do I begin with this question. I've tried some wild attempts but they landed me no where :-( Can you please guide me with the solution to this question? [/B]

 

[Qwertywerty]

I've tried some wild attempts but they landed me no where :-

Please post these attempts .

However I still give a hint :

What does dy/dx represent ?
What is the formula for Range ?

 

[andrevdh]

The angle of projection can be found from the gradient of the graph at what point?

 

[dahano]

I figured out the formula for Ran

Please post these attempts .

However I still give a hint :

What does dy/dx represent ?
What is the formula for Range ?

I figured out the formula of range as: u²Sin2(theta)/g

Can you tell me that how would it be done further?

 

[dahano]

The angle of projection can be found from the gradient of the graph at what point?

Sorry to ask a stupid question but what do you mean by point? Can you please show me how would it be solved?

 

[Qwertywerty]

I figured out the formula of range as: u2Sin2(theta)/g

Can you tell me that how would it be done further?

Here - dy/dx at x = 0 represents tan(θ) ( where θ is angle of projection ) .

Find range , and then using formula for range find u .

 

[andrevdh]

What does the trajectory or path of the projectile look like?
What is the equation which describes the path or trajectory?

 

[NascentOxygen]

I figured out the formula of range as: u²Sin2(theta)/g

Please attach your working for this.