A large firework shell is moving vertically upward at the moment when it explode

Question

A large firework shell is moving vertically upward at the moment when it explodes into three pieces of

unequal mass. At the moment right after the explosion, piece 1 is moving horizontally westward, and piece 2 is moving

horizontally eastward.Evaluate the following statements (True/False/Not Enough Information):

a. The velocity of piece 3 right after the explosion must be vertically upward.

b. The Speed of piece 3 right after the explosion could be greater than the speed of the whole shell right before the explosion.

c. The velocity angle of piece 3 right after the explosion could not be below the horizontal.

Explanation / Answer

a) false,it is not necessary that the velocity of the piece three will be vertically upward right after the explosion. it must have a vertical component of velociy vertically upward but the horizontal component may not be zero.

b) True, if the mass of the shell is Ms and mass of piece 3 be M3,

by conservation of momentum in vertical direction, Ms*Vs = M3*V3

(where Vs and V3 are the vertical velocities )

we get, V3 = Vs*(Ms/M3) which is greater than Vs as Ms>M3.

also it may also have a horizontal component of its velocity which will lead to further incriment in speed.

c) true , there was momentum in vertically upward direction initially,and there was no momentum in vertically downward direction, so by conservation of momentum, after the explosion there will be no momentum in vertically downward direction. therefore piece 3 cannot have its velocity angle below horizontal as it will lead to a momentum in vertically downward direction which is violation of conservation of momentum law. ( as the other two pieces also do not have any momentum in vertical direction)

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