Question

A spaceship of mass 2.0×10⁶ kg is cruising at a speed of 4.9×10⁶ m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 4.6×10⁵ kg , is blown straight backward with a speed of 2.1×10⁶ m/s . A second piece, with mass 8.2×10⁵ kg , continues forward at 1.3×10⁶ m/s .

What is the speed of the third piece?

Answer 1

Here,

let the third piece has speed v

Using conservation of momentum

initial momentum = final momentum

2 *10^6 * 4.9 *10^6 = 4.6 *10^5 * (-2.1 *10^6) + 8.2 *10^5 * 1.3 *10^6 + (2 *10^6 - 4.6 *10^5 - 8.2 *10^5) * v

solving for v

v = 1.34 *10^7 m/s

the speed of the third piece is 1.34 *10⁷ m/s