Physics explosions and recoil speed?

Question

a cannon with mass 400 kg sits atop a narrow wall and horizontally launched an aid packet to hungry villagers a distance 2km away. someone forgot to lock the wheels of the cannon and the recoil causes it to roll backwards off the wall. if the aid packet has a mass of 10kg and there is no friction in the wheel bearings of the cannon, how far does the cannon land behind the wall?

billrussell42 · Accepted Answer

you would use conservation of momentum, but in order to find the velocity of the packet, you would need the height of the wall. If you have that, use that plus the 2000 meter distance to get the launch speed, which gives you the momentum of the packet. that is set equal to the momentum of the cannon, which gives you the speed the cannon is pushed back, from which you can get, if you have the height of the wall, you can get the landing point of the cannon.

Perhaps I can leave the height as symbolic, h.

flight time is t = √(2h/g)
speed is d/t = 2000 / √(2h/g)
momentum is 10•2000 / √(2h/g)
which is momentum of cannon, equal to mass x velocity
V = (1/400)10•2000 / √(2h/g) = (50) / √(2h/g)
time in air is same as above t = √(2h/g)
and distance is Vt = √(2h/g) [ (50) / √(2h/g)  ]

and h does indeed cancel
d = 50 meters ⬅

and you can get that from the ratio of masses x distance 
d = (2000)(10/400) = 50 meters  ⬅

Physics explosions and recoil speed?

1 Answer