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14. A car P is moving with a uniform speed of 5√3 m/s towards a carriage of mass 9 Kg at rest kept on the rails at a point B as shown in figure. The height AC is 120 m. Cannon balls of 1 Kg are fired from the car with an initial velocity 100 m/s at an angle 30o with the horizontal. The first cannon ball hits the stationary carriage after a time t0 and sticks to it. Determine t0. uniform-motion At t0, the second cannon ball is fired. Assume that the resistive force between the rails and the carriage is constant and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks to the carriage, what will be the horizontal velocity of the carriage just after the second impact?

14. A car P is moving with a uniform speed of 5√3 m/s towards a carriage of mass 9 Kg at rest kept on the rails at a point B as shown in figure. The height AC is 120 m. Cannon balls of 1 Kg are fired from the car with an initial velocity 100 m/s at an angle 30o with the horizontal. The first cannon ball hits the stationary carriage after a time t0 and sticks to it. Determine t0. uniform-motion At t0, the second cannon ball is fired. Assume that the resistive force between the rails and the carriage is constant and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks to the carriage, what will be the horizontal velocity of the carriage just after the second impact?

Grade:11

1 Answers

Nishant Bhardwaj
16 Points
4 years ago
Vertical motion of the first cannon ball--
-120=100sin30 t°-- (0.5)gt°^2
t°=12sec.
 
Horizontal motion of the first cannon ball 
Let it be x
x=100cos30t°=600√3 meter
For the carriage conserving the momentum in horizontal direction
1×50 √3={9+1}v . => v=5√3 m/s
Vertical motion of II cannonball is identical to the first ball so,  t°=12 sec
 
Horizontal motion of II cannonball 
x-5√3 t°+5√3 t -(0.5)at^2 =100 cos30 t
==> a=0
Conserving the momentum in horizontal direction again for the carriage 
(9+1)5√3 +1(50√3) =(9+1+1)v 
So, v=(100√3)/11 .m/s
 
 
 
 
 
 

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