Question

2 guns,situated on the top of a hill of height 10m,fire 1 shot each with the same speed 5 31/2 m/s at some interval of time. 1 gun fires horizontally and other fires upwards at an angle of 60 with the horizontal.the shots collide in air at point P. find the time interval between the firings,and the coordinates of the point P.Take origin of the coordinate system at the fot of the hill right below the muzzle and trajectories in x-y plane.

Answer 1

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 coordinates 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)