A body is projected from ground level with speed v0 at an angle θ0 to the horizontal.
(a) Starting from first–principle equations of motion, derive an expression for the total time of flight T.
(b) Using the result of part (a), obtain a formula for the horizontal range R.
(c) Prove that, for a given v0, the range is maximum when θ0=45∘ and determine this maximum value.
a. (a) Derivation of total time of flight
b. (b) Derivation of horizontal range
c. (c) Proof of condition for maximum range and expression for Rmax