A shell is fired from a canon with a velocity v(m/sec) at an angle x with the horizontal.At the highest point in its path, it explodes into 2 pieces of equal masses.One of the piece retraces into the cannon then the speed in m/sec of the other piece immediately after the explosion is;
(a)3v cos x
(b)2v cos x
(c)1.5v cos x
(d)1.5^2v cos x

Vaibhav Mathur, 14 years ago

Grade:12

7 Answers

AskiitianExpert Shine

10 Points

14 years ago

ans: 3vcosx

At the top of its path, vel is vcos x only in horizontal direction , so after explosion to retrace its path , the velocity of one of the equal masses should be -vcos x . therefore now if v conserve the momentum, then 2mvcosx = -mvcosx + mv' . calculate v' .

Pratham Ashish

17 Points

14 years ago

hi vaibhav,

dis question is quite straight forward

as velocity at d highest point is v cosx

just apply momentum conservation

m(v cosx) = m/2 (-ucosx ) + m/2 v1, [ as it is divided into parts of equal mass n one part retraces to d cannon itself so its velocity will be vcosx but wid a negative sign]

we hav to find v1

here simply u get v1= 3v cosx

moidin afsan

20 Points

10 years ago

Let ‘2m’ be the mass of the cannon which is projected with velocity ‘v’ at an angle ‘?’ with the horizontal. The horizontal component of the velocity of the cannon is, vx = v cos?. This component remains constant. At the maximum height, the cannon has only this component as the vertical component is momentarily zero. So, momentum before exploding = 2mv cos? After exploding, one of the masses retraces the path of the cannon backwards. This is possible on if the part has velocity ‘-v cos?’. Therefore, momentum after explosion = -mv cos? + mu So, by conservation of momentum, 2mv cos? = -mv cos? + mu = > u = (3v cos?) m/s

Sankalp Goyal

36 Points

7 years ago

Let ‘2m’ be the mass of the cannon which is projected with velocity ‘v’ at an angle ‘?’ with the horizontal. The horizontal component of the velocity of the cannon is, vx = v cos?. This component remains constant.At the maximum height, the cannon has only this component as the vertical component is momentarily zero.So, momentum before exploding = 2mv cos?After exploding, one of the masses retraces the path of the cannon backwards. This is possible on if the part has velocity ‘-v cos?’.Therefore, momentum after explosion = -mv cos? + muSo, by conservation of momentum,2mv cos? = -mv cos? + mu= > u = (3v cos?) m/s

Sankalp Goyal

36 Points

7 years ago

Let ‘2m’ be the mass of the cannon which is projected with velocity ‘v’ at an angle ‘?’ with the horizontal. The horizontal component of the velocity of the cannon is, vx = v cos?. This component remains constant.At the maximum height, the cannon has only this component as the vertical component is momentarily zero.So, momentum before exploding = 2mv cos©After exploding, one of the masses retraces the path of the cannon backwards. This is possible on if the part has velocity ‘-v cos?’.Therefore, momentum after explosion = -mv cos? + muSo, by conservation of momentum,2mv cos? = -mv cos© + mu= > u = (3v cos©)m/s

Sankalp Goyal

36 Points

7 years ago

Dear friends,By conservation of momentumInitial momentum = Final momentumInitially the mass of Canon is 2m and its horizontal component is vcosxInitially mass of Canon is taken because at that time the bullet is not explode into two partsBut the final momentum of bullet is break down into two parts the two particles which explodes both have same mass but have different velocities.The one which retraced is path have velocity -vcosx and we have to find velocity of second particleInitial momentum=Final momentum2mvcosx = -mvcosx + mumu = 2mvcosx + mvcosxmu = m(2vcosx + vcosx)u = 3vcosx(1) ........

Kushagra Madhukar

askIITians Faculty 628 Points

3 years ago

Dear student,

Please find the solution to your solution to your problem below.

At the top of its path, vel is vcos x only in horizontal direction , so after explosion to retrace its path , the velocity of one of the equal masses should be -vcos x . therefore now if we conserve the momentum,

then 2mvcosx = -mvcosx + mv

Therefore, v = 3vcosx

Hope it helps,

Thanks and regards,

Kushagra