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A body is projected vertically upwards. At its highest point it explodes into 2 pieces of masses in the ratio 2:3 and the lighter piece flies horizontally wih a velocity of 6metre per second.The time after which the lines joining the point of explosion to the position of particlesd are perpendicular to each other is(g=10m/ssq.)?

A body is projected vertically upwards. At its highest point it explodes into 2 pieces of masses in the ratio 2:3 and the lighter piece flies horizontally wih a velocity of 6metre per second.The time after which the lines joining the point of explosion to the position of particlesd are perpendicular to each other is(g=10m/ssq.)?

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
Let the body be projected with a velocity v along the vertical direction.
The height reached by the body be given by:
h=\frac{v^{2}}{2g}
The the mass of the body be 5m kg.
So the initial momentum of the body be:
p_{y}=5mv
After the body breaks into two parts, the momenta of the particles be:
p_{2}=2m\times 6=12m
p_{3}=3m\left ( v_{x}+v_{y} \right )
Using conservation of momentum, we have:
0=12m+3mv_{x}, 5mv=3mv_{y}
Solving these would give the velocities of both the particles and then using conservation of energy, the ddistance of each particle can be found.
Regards
Sumit

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