In the impoverished mountain kingdom of Pontevedro, the Royal Artillery has deve
ID: 2258783 • Letter: I
Question
In the impoverished mountain kingdom of Pontevedro, the Royal Artillery has developed a method to
conserve gunpowder: its cannon is fired horizontally from a cliff, with the muzzle velocity controlled so
that the cannonball will strike the target on the plain below on the second bounce. The two Royal
Engineers agree that on the first bounce, the ball loses 40% of its vertical speed, but none of its horizontal speed.
(a) If the cliff is 1 km high, what muzzle speed is needed to hit a target 9 km from the base of the
cliff?
(b) If the initial energy of the cannonball is proportional to the mass of gunpowder used, what is
the percentage of gunpowder saved by the Royal Bounce method?
In the impoverished mountain kingdom of Pontevedro, the Royal Artillery has developed a method to conserve gunpowder: its cannon is fired horizontally from a cliff, with the muzzle velocity controlled so that the cannonball will strike the target on the plain below on the second bounce. The two Royal Engineers agree that on the first bounce, the ball loses 40% of its vertical speed, but none of its horizontal speed. If the cliff is 1 km high, what muzzle speed is needed to hit a target 9 km from the base of the cliff? If the initial energy of the cannonball is proportional to the mass of gunpowder used, what is the percentage of gunpowder saved by the Royal Bounce method?Explanation / Answer
as it doesnt lose its horizantal speed on bounce
range=sum of ranges of two projectile motions
A)
9*1000m=v^2/2g+v^2(sin2x)/g
tan x=.4Vy/Vx
Vy=Vx/g * g
Vy=Vx
tan x=0.4
sin 2x=.689
9000=V^2/g (0.5 + 0.689)
Vx^2 = 9000/.121
Vx=272.7m/s
B)
if this method is not used
Vx^2/2g=9000
Vx^2=176400 (m/s)^2
V(normal) - V(new method) / V(normal) * 100 is %saved
=.5799*100
=58%
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