A 6.00 kg model rocket is traveling horizontally and due south with a speed of 2
ID: 1309114 • Letter: A
Question
A 6.00 kg model rocket is traveling horizontally and due south with a speed of 24.0 m/s when it explodes into two pieces. The velocity of one piece, with a mass of 1.70 kg, is v1 right arrow = ( - 12.0 m/s )i^ + ( 37.0 m/s )j ^- ( 14.0 m/s )k^ , with i^ pointing due east, j^ pointing due north, and k^ pointing vertically upward, (a) What is the linear momentum of the other piece, in unit-vector notation? (b) What is the kinetic energy of the other piece? (c) How much kinetic energy is produced by the explosion?Explanation / Answer
a) By conservation of momentum , 6*24(-i) = 1.7(-12i+37j-14k)+p
On solving , p= -144i-1.7(-12i+37j-14k) = -123.6i-62.9j+23.8k
b) kinetic energy = p.p/2m ( dot indicates dot product) = p.p/2(24-1.7) =140.712^2/(2*22.3) = 443.9
c) kinetic energy produced = initial kinetic energy - kinetic energy of each fragment
= 1/2*6*24*24 - 443.9 - 502.64 = 781.46