Loving the scientific model Ace
I have to disagree though, I don't think it is a semi circle. Just to clarify, I'm talking about the bit above point of explosion, ie the upper half.
It doesn't need saying that the maximum height reached will be the fragment fired at 90
o from the horizontal. To calculate the distance, I rearranged one of the SUVAT equations:
V
2 = U
2 + 2AS
To give:
S = (V
2 - U
2)/2A
Inputting our data, we get:
S = (0
2 - 20
2)/2*-9.81
S = 20.38735984m
I also did it with V=U+AT and S=UT+0.5AT
2 and got the same result.
Now, calculating how wide the blast radius is:
These are the y-components of the projectile:
V=U+AT => 0=20sin(45)-9.8t => t=1.441604039s
(I worked it out the long way, calculating time first, because I thought it would be useful to know time for other calculations)
Then with the x-components:
s=20cos(45)t (from S=UT+0.5AT
2 , A=0 as it's the x-component so S=UT)
s=20.38735984m
But this is only to the point where the projectile is at its max height, ie in the middle, so we double it to get:
40.77471968m
If it was a semi circle, then the radius would be the same all around the origin :)
Tom