The battleship Massachusetts' 16" guns could fire a 1-ton shell with an initial velocity of 800m/s. If it fired its guns at an angle of 45 degrees above horizontal, how high and how far would the shells travel?
I'm pretty sure that I need to use the Pythagorean Theorem, but I'm not quite sure how to use it in this scenario. If someone could just explain to me and walk me through how to do this, that would be much appreciated.
Thanks in advanced. :)
Vertical velocity:
800*sin45 m/s
determine the time of flight
hf=hi+vi'*t-4.9t^2
0=0+800sin45*t-4.9t^2
t(800sin45-4.9t)=0
t=800sin45/4.9 seconds.
Now,
how high: max height occurs at t/2, so
h=vi*t-1/2 g t^2 where t=tabove/2
how far?
distance=800cos45*timeinair
My experience with the Iowa, it doesn't actually shoot that far, due to air resistance, but about 32 miles max.
Max altitude? Yep, one has to put out air hazard advisories.