Question

A missile in space is traveling at a speed of 1.00×10⁵ m/s along the positive x- axis. The missile breaks into two pieces during an explosion. The larger of the two pieces has a mass that is 80.0 % of the mass of the entire missile. The two pieces separate at different angles with respect to the direction of the initial velocity of the missile before the explosion. Piece 1, the larger, breaks away at an angle of 14.0 degrees , while piece 2 at an angle of -5.00 degrees . If all angles are given with respect to the positive x axis. Find the final speed of piece 1 (v1) and piece 2 (v2) of the missile.

Answer 1

Let the mass of the missile be m. Its initial speed was v = 10^5 m/s along positive x-axis. The missile breaks into two pieces. Let thE mass of the larger piece be m1 and that of the smaller piece be m2. Given m1 is 80% of m. Therefore,

By mass conservation,

The mass m1 breaks away at an angle of 1 = above the x-axis and the mass m2 reaks away at an angle of 2 = below the x-axis. Let v1 and v2be the final velocity of m1 and m2.

Now applying momentum conservaton along the y-direction,

Applying momentum conservaton along the x-direction,

So the final speed of piece 1 and piece 2 of the missile are 3.73 x 10^4 m/s and 35.43 x 10^4 m/s respectively.