A 5.1 kg model rocket is traveling horizontally and due south with a speed of 21.6 m/s when it explodes into two pieces.

Question

A 5.1 kg model rocket is traveling horizontally and due south with a speed of 21.6 m/s when it explodes into two pieces. The velocity of one piece, with a mass of 1.6 kg, is

v₁ = (-12 m/s)i + (30 m/s)j + (15 m/s)k,

with i pointing due east, j pointing due north, and k pointing vertically upward.

(a) What is the velocity of the other piece, in unit-vector notation?

 m/s i

 m/s j

 m/s k

(b) What is the kinetic energy of the other piece?

 J

(c) How much kinetic energy is produced by the explosion?

 J

Answer 1

Hi Abdi F.,

Momentum is conserved in each axis. So solve them individually. Kinetic energy is the Pythagorean-theorem diagonal of all 3-D vector components, as (1/2)m (v)^2.

Total kinetic energy release is likely to include substantial loss to product gases of the explosion, and kinetic energy of rotation and vibration of the 2 pieces, also unknown. A minimum bound would be the sum of the 2 pieces' KE's.

If you had been carrying the model rocket, how much KE could YOU have absorbed? Unfortunately, there are data on fireworks accidents. You might term it, "previous digital information"? ....

--Cheers, --Mr. d.