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

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.