Step-by-step explanation:
Consider the vertical motion of ball,
We have equation of motion v = u + at
Initial velocity, u = u sin θ
Final velocity, v = -u sin θ
Acceleration = -g
Substituting
v = u + at
-u sin θ = u sin θ - g t
This is the time of flight.
Consider the vertical motion of ball till maximum height,
We have equation of motion v² = u² + 2as
Initial velocity, u = u sin θ
Acceleration, a = -g
Final velocity, v = 0 m/s
Substituting
v² = u² + 2as
0² = u²sin² θ + 2 x -g x H
This is the maximum height reached,
Consider the horizontal motion of ball,
Initial velocity, u = u cos θ
Acceleration, a =0 m/s²
Time,
Substituting
s = ut + 0.5 at²
This is the range.
For maximum range
sin 2θ = 1
2θ = π/2
θ = π/4
For maximum range, θ = π/4
