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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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