Arock is thrown upward from level ground in such a way that the maximum height of its flight is equal to its horizontal range r.

(a) at what angle theta is the rock thrown?

(b) in terms of its original range r, what is the range r_max the rock can attain if it is launched at the same speed but at the optimal angle for maximum range?

(c) would your answer to part (a) be different?

(a) Θ =

(b) is achieved when T = , thus = R ÷ Sin2T

(c) Yes

Explanation:

(a)  Max. height () =

     Range (R) =

where T represents theta

So for, R =

⇒   =

Using trigonometric functions,

        = 2SinTCosT =

  ⇒ 4 = Tan T

        T =

           =

∴ Theta =

(b) Since,  R =

is achieved when T =

=

∴     = R ÷ Sin2T

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