Question

a 46.0-$kg$ body is moving in the direction of the positive x axis with a speed of 243 $m/s$ when, owing to an internal explosion, it breaks into three pieces. one part, whose mass is 8.0 $kg$, moves away from the point of explosion with a speed of 412 $m/s$ along the positive y axis. a second fragment, whose mass is 5.0 $kg$, moves away from the point of explosion with a speed of 445 $m/s$ along the negative x axis. what is the speed of the third fragment? ignore effects due to gravity.

Answer 1

To find the velocity of the third fragment, you can apply the law of conservation of momentum. Set the initial momentum equal to the final momentum and substitute the given values to solve for the velocity of the third fragment and we get (11178 kg·m/s) / (mass3).

Step-by-step explanation:

To solve this problem, we can apply the law of conservation of momentum. Momentum is a vector quantity, so we can write it as:

pinitial = pfinal

Before the explosion, the momentum of the 46.0 kg body is:

pinitial = (mass1)(velocity1)

pinitial = (46.0 kg)(243 m/s) î

After the explosion, the momentum of the three fragments can be written as:

pfinal = (mass1)(velocity1) + (mass2)(velocity2) + (mass3)(velocity3)

Substituting the known values, we have:

(46.0 kg)(243 m/s) î = (8.0 kg)(0 m/s) î + (5.0 kg)(-445 m/s) î + (mass3)(velocity3)

Simplifying and isolating the velocity of the third fragment, we can solve for it:

(46.0 kg)(243 m/s) î - (8.0 kg)(0 m/s) î - (5.0 kg)(-445 m/s) î = (mass3)(velocity3)

velocity3 = [(46.0 kg)(243 m/s) - (5.0 kg)(-445 m/s)] / (mass3)

Substituting the given values, we can calculate the velocity of the third fragment:

velocity3 = (11178 kg·m/s) / (mass3)