Answer to Question #152388 in Physics for Amelia

Question #152388
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 tt can be found from the kinematic equation (if there is no vertical initial velocity component):



h=gt22h = \dfrac{gt^2}{2}

where h=100mh = 100m is the height, and g=9.8m/s2g = 9.8m/s^2 is the gravitational acceleration. Thus, obtain:


t=2hg=21009.84.5st = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2\cdot 100}{9.8}} \approx 4.5s

In this time the stone covers the following horizontal distance:


d=v0t=540m/s4.5s2439md = v_0t = 540m/s\cdot 4.5s\approx 2439m

Here v0=540m/sv_0 = 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=5.44kgm = 5.44kg is given by the expression:


pball=mv0pball=5.44540=2937.6 kgm/sp_{ball} = mv_0\\ p_{ball} = 5.44\cdot 540 = 2937.6\space kg\cdot 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=pballp_{recoil} = p_{ball}\\ m_{recoil}v_{recoil} = p_{ball}\\

where mrecoil=5000kgm_{recoil} = 5000kg is the mass of the cannon. Then the velocity of the recoil is:


vrecoil=pballmrecoilvrecoil=2937.650000.59m/sv_{recoil} = \dfrac{p_{ball}}{m_{recoil}}\\ v_{recoil} = \dfrac{2937.6}{5000} \approx 0.59m/s

Answer. (a) 2439 m, (b) 2937.6 kg*m/s, (c) 0.59 m/s.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment