After several large firecrackers have been inserted into its holes, a bowling ba

Question

After several large firecrackers have been inserted into its holes, a bowling ball is projected into the air using a homemade launcher and explodes in midair. During the launch, the 4-kg ball is shot into the air with initial speed v0 = 11.4 m/s at angle ? = 42°; it explodes at the peak of its trajectory, breaking into three pieces of equal mass. One piece travels straight up with a speed of 3.0 m/s. Another piece travels straight back with a speed of 2.0 m/s. What is the velocity of the third piece (speed and direction)? (Let up be the +y-direction and to the right be the +x-direction.)
speed: ???? m/s and direction: ????? degree below the horizontal.

Explanation / Answer

at the top of the projectile velocity of 4-kg projectile is 11.4cos42 = 8.4718m/s i now applying conservation of momentum just before and after the explosion for the entire system momentum before explosion Pi = 4*8.4718 = 33.8874kgm/s i after explosion velocity of one piece is 3m/s j another piece is 2m/s (-i) here i and j denote unit vectors along positive x and y directions respectively now final momentum is (4/3)*(3j) + (4/3)*(-2i) + (4/3)*(v) now equating initial and final momentum we get v as v = 27.4155i -3j m/s

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