Question

The range of the target is found to be 30km. A shell leaves a gun with a velocity of 500ms-1 . what must be the angles of elevation of the gun,If the gun is level? In physics

Answer 1

If the gun is level? ???It is not level.
angle above horizontal = b
speed = 500
Horizontal problem:
u = 500 cos b m/s
range = u t = 30,000 meters
so
t = 30,000 / 500 cos b = 60 cos b
Vertical problem:
Vi = 500 sin b
v = Vi - g t
h = Vi t - (1/2) g t^2
at ground h = 0
so
0 = t (Vi - .5 g t)
so
t = Vi /.5 g = 500 sin b /.5 g = 1000 sin b / g
so
1000 sin b / g = 60 cos b
sin b / g = 60 / 1000 cos b
sin b cos b = 60 g/1000 = 0.5886
2 sin b cos b = 1.17 = sin 2 b
no angle has a sin >1
You need more gunpowder I think.