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canon ball is fired with a velocity 200 m/s at an angle of 60o with horizontal . At highest point of its flight it explodes into 3 equal fragments , one going vertically upwards with a velocity 100 m/s , the second falling vertically downwards ...

canon ball is fired with a velocity 200 m/s at an angle of 60o with horizontal. At highest point of its flight it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/s, the second falling vertically downwards ...

Grade:11

1 Answers

Saravan V
34 Points
8 years ago

Resolve the motion of the cannon ball into vertical and horizontal components.
Horizontal component of velocity V(x) = V cos60 =  V/2 = 100 m/s
Vertical component of velocity V(y) = V sin60 = 100√3 m/s

At the topmost point, the velocity is purely horizontal, i.e, the vertical component becomes zero due to deceleration produced by the earth''s gravity.
Let the mass of the original object be M.
Applying Principle of Conservation of Momentum,

Momentum in vertical direction before explosion = Momentum in vertical direction after collision.

M*0 = M/3*100 + M/3(velocity of verticallf falling fragment)

=> Velocity of vertically falling fragment is 100 m/s downwards.

Momentum in horizontal direction before explosion = Momentum in horizontal direction after explosion.

M*100 = M/3*(Velocity of third fragment)

Hence velocity of third fragment is 300 m/s towards right. 

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