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Calculations on an Exploding Projectiles

An instrument carrying projectile accidentally explodes at the top of its trajectory. The horizontal distance between the launch point and the point of explosion is L. The projectile breaks into pieces which fly apart horizonally. The larger piece has three times the mass of the smaller piece. To the surprise of the scientist in charge, the smaller piece returns to earth at the lauching station. How far away does the larger piece land? Neglect air resistance and effects due to the earth's curvature

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Since we're given information about the small particle, if we can figure out its velocity, we can use conservation of momentum to deduce the velocity of the other particle. Then we can figure out how far away it landed.

Now, start by assuming that it took time t for the particle to fall to earth. Then we know the speed in the x-direction is given by:
Speed = distance/time = L / t

The velocity would be the negative of this, since the particle is traveling in the negative x-direction.

Now we can use the law of conservation of momentum to determine the velocity of the large particle ...

Solution Summary

An instrument- carrying projectile is examined as per the question in 436 words with fully-explained calculations.