A cannon from the Napoleonic wars was able to launch cannon balls at a velocity of 540 m s–1. The cannon is fired at the top of a cliff with the barrel in the horizontal position.
(a) Neglecting air resistance, what is the range of the cannon ball, to the point where it hits the water 100 m below?
(4 marks)
(b) Calculate the initial horizontal component of the momentum of the cannon ball, if it has a mass of 5.44 kg. (2 marks)
(c) If the cannon has a mass of 5000 kg and is on a trolley on the horizontal surface, what is its initial recoil velocity?
(2 marks)
1
Expert's answer
2020-12-23T07:35:19-0500
(a)Time of falling t can be found from the kinematic equation (if there is no vertical initial velocity component):
h=2gt2
where h=100m is the height, and g=9.8m/s2 is the gravitational acceleration. Thus, obtain:
t=g2h=9.82⋅100≈4.5s
In this time the stone covers the following horizontal distance:
d=v0t=540m/s⋅4.5s≈2439m
Here v0=540m/s is the initial horizontal velocity of the ball.
(b) The initial horizontal component of the momentum of the cannon ball of mass m=5.44kg is given by the expression:
pball=mv0pball=5.44⋅540=2937.6kg⋅m/s
(c) The initial recoil momentum is equal to the initial horizontal component of the momentum of the cannon ball (according to the momentum conservation):
precoil=pballmrecoilvrecoil=pball
where mrecoil=5000kg is the mass of the cannon. Then the velocity of the recoil is:
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