A large, lit m80 (a type of firework) is dropped off of a bridge. When the m80 is 12.30 m below the its drop point, it is moving with a speed of 12.30 m/s down. At this point the m80 explodes into two pieces, one piece with a mass of 0.265 kg moves downward with a speed of 18.90 m/s, and the other piece has a mass of 0.350 kg. If mass is conserved, what are the speed and direction of the 0.350 kg piece after the explosion? Ignore wind resistance.
A large, lit m80 (a type of firework) is dropped off of a bridge. When the m80 is 12.30 m below the its drop point, it is moving with a speed of 12.30 m/s down. At this point the m80 explodes into two pieces, one piece with a mass of 0.265 kg moves downward with a speed of 18.90 m/s, and the other piece has a mass of 0.350 kg. If mass is conserved, what are the speed and direction of the 0.350 kg piece after the explosion? Ignore wind resistance.
Consider the following diagram,
Given the mass is conserved. Therefore the mass of lit M-80 will be the sum of masses of the two pieces. Let v be defined as the velocity of a piece having mass 0.350 kg, and the direction of the velocity be defined as θ. Let u be defined as the initial velocity, and it is defined as 12.30 m.s-1.
Using the conservation of momentum,
Comparing the x-component and y-component,
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