Two guns ,situated on the top of a hill of height 10 m ,fire one shot each with the same speed 5root 3 m/s at some interval of time .One gun fires horizontaly and other fires upwards at an angle of 60 with the horizontal .The shots collides in mid air at pt. P. Find 1)the time interval btw firing 2)the coordinates of pt. P.(take origin at foot of hill right below muzzles and trajectories in x-y plane). pls give full sol.

Dear jyoti ,

write equations of motion for both the guns

gun2:fires at t=0

x direction : x =5root3 * cos 60 * (t )   

y direction : y =  5root3sin60(t) - 1/2 *g *(t)²

gun1:fires at t=t1

x direction : x =5root3 *(t-t1)   

y direction : y =  - 1/2 *g *(t-t1)²   (negative as upward direction is positive

 

when they collide their x and y cordinates are equal ,

so if  they collide at t=t2 then ,

5root3 *t2-t1= 5root3 * cos 60 * (t2 )   

- 1/2 *g *(t2-t1)²  =  5root3sin60(t2) - 1/2 *g *(t2)²  

solving we get ,

t2= 2s , t1 =1s

so 1) time interval b/w firing  =t1 =1s

   2)p = (5root3 *(2-1) ,  -1/2*g*(2-1)² )

      p =(5root3 , -5)

                                                                    
                                                                     
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Find trajectory eqn of both then equate it then solve it. Then u will get x and then u can find t1 and t2