2. During the siege of Constantinople that led to its conquest by the Ottomans i

Question

2. During the siege of Constantinople that led to its conquest by the Ottomans in 1453, the Hungarian engineer Orban built a set of bombards (primitive cannon) to throw enormous stones at the city to breach its walls. The largest of these could throw a 300 kg stone a distance xf = 2 km. Assume that the stone was launched at an angle of = 45 above the horizontal; in the absence of air resistance, this gives the largest range. (a) What speed did the stone have to be launched at to achieve this range? (b) How long was the ball in the air? (c) How fast was the ball traveling at the apex of its flight? (d) Orban’s cannon was 8m long. What was the average acceleration of the stone as it was launched down the bore of the cannon? Hint: Note that during its movement down the bore of the cannon, it accelerated from v = 0 to the velocity you found as your solution to the first part of this problem.

Explanation / Answer

part a:

range of a projectile=v^2*sin(2*theta)/g

where v=initial speed

then 2000=v^2*sin(2*45)/9.8

==>v=140 m/s

so the stone has to be launched with a speed of 140 m/s.

part b:

time of travel=2*v*sin(theta)/g

=2*140*sin(45)/9.8=20.203 seconds

part c:

at the maximum height, vertical component of speed=0

only horizontal component remains.

as horizontal acceleration is 0 ,

horizontal speed is constant and hence equal to intiial horizontal speed=140*cos(45)=99 m/s

part d:

initial speed=0

final speed before launch=140 m/s

acceleration=a m/s^2

distance=8 m

using the formula:

final speed^2-initial speed^2=2*acceleration*distance

==>140^2-0^2=2*a*8

==>a=1225 m/s^2

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