The M777 lightweight 155mm howitzer is a piece of artillery whose rounds are eje

Question

The M777 lightweight 155mm howitzer is a piece of artillery whose rounds are ejected from the gun with a speed of 829m/s. Assuming that the gun is fired over a flat battlefield and ignoring aerodynamic effects, determine a) the elevation angle needed to achieve the maximum range, b) the maximum possible range of the gun, and c) the time it would take a projectile to cover the maximum range. Express the result for the range as a percentage of the actual maximum range of this weapon, which is 30 km for unassisted ammunition.


I tired to find the angle and got 90 degrees, but I don't think its right.
Please help!!!

Explanation / Answer

v = 829 m/s, angle =

at the range d, vertical displacement = 0

so vsin*t = gt2/2 = 0

t = 2vsin/g

d = vcos*t = vcos*2vsin/g = v2*(2sin cos)/g = v2*sin(2)/g

for maximum d, sin(2) is maximum which is 1 when 2 = 90o, so

dmax = v2/g = 8292/9.81 = 7.01*104 m = 70.1 km

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