Battleship Yamato
Please help solve physics projectile motion problem?
The largest naval guns ever built, on the Japanese world War II battleship Yamato and her sister Musashi, had a range of 42 km when fired at an angle 45 degrees above the horizontal.
a) Ignoring air resistance and the curvature of the earth, what muzzle velocity (the speed of the shell as it leaves the gun) is necessary to achieve this range?
b) The Yamato’s guns were 21 m long. What was the average acceleration undergone by the shells as they were fired?
Let:
t be the flight time,
u be the muzzle velocity,
a be the average acceleration provided by the guns.
(a)
Resolving horizontally and vertically:
42 = ut cos(45) …(1)
0 = ut sin(45) – 9.81t^2 / 2 …(2)
Substituting for t from (1) in (2):
0 = 42 tan(45) – 9.81 * 42^2 / 2u^2 cos^2(45)
42 = 9.81 * 42^2 / u^2
u^2 = 9.81 * 42
u = 20.3 m/s.
(b)
u^2 = 2a * 21
a = 9.81 m/s^2.
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