A875-kg two-stage rocket is traveling at a speed of 6.55×103 m/s away from earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.50×103 m/s relative to each other along the original line of motion. a)what is the speed of each section (relative to earth) after the explosion? b)how much energy was supplied by the explosion? [hint: what is the change in kinetic energy as a result of the explosion?

Answer

gives,

mass of the rocket = M = 875 Kg

speed of the rocket before explosion (V) = 6.55 x 10³ m/s

rocket divide into two parts

mass of first part (m₁) = 875/2 = 437.5 Kg

mass of second part (m₂) = 437.5 Kg

relative speed between two section

v₁ - v₂ = 2.5 x 10³ m/s................(1)

using energy of conservation

M V = m₁ v₁ + m₂ v₂

875 x 6.55 x 10³ = 437.5 (v₁ + v₂)

v₁ + v₂ = 13.1 x 10³......................(2)

adding equation (1) and (2)

2v₁ = 15.6 x 10³ m/s

v₁ = 7.8 x 10³ m/s

v₂ = 5.3 x 10³ m/s

b) Energy supplied by explosion

 E = Final energy - initial energy

E = 683 x 10⁶ J

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer