A projectile is fired with a speed u at an angle θ above a horizontal field. The coefficient of restitution of collision between the projectile and the field is e. How far from the starting point, does the projectile makes its second collision with the field?

The projection velocity is v,

The projection angle is Ө,


Acceleration due to gravity g = 10 m/s,


When the projectile hits the ground for 1st time, the velocity would be same i.e., u.


Here the component of velocity parallel to the ground should remain constant.


But the vertical component of velocity undergoes a change after collision.


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Now for 2nd projectile motion


Velocity of projection,



And angle of projection,




Or _________ (1)


Because equation for path of projectile motion


__________ (2)


Here, y = 0,


And


Putting these values in equation (2)






So, from starting point O the projectile makes its second collision with the field at a distance x’




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