Two balls are fired form ground level,`a` distance `d` apart. The right one is fired vertically with speed `v`. You wish to simultancously fire the left one at appropriate velocity `u` so that collides with the right ball when they reach their highest point. Value of horizontal `(u_(x))` and vertical `(u_(y))`components of `u` are respectively`:-`
.

Answer

`0010.00`

Explanation

The vertical speeds must be equal at the start and have always Rightarrow u=V This is time because the two y values are given by `u_(1) t-1/2 gt^(2) and Vt-1/2 gt^(2) Rightarrow we must have u_(1)` =V if these are to be equal for same (and hence all)t
To find the horizontal speed note that the balls take a time `T=v//s` to reach the temp.
The left ball must travel a horizontal distance d in this time Rightarrow `u_(g)=d/(v//g)= Rightarrow vec(u)=((gd)/v,v)`
`u=sqrt(g^(2)d^(2))/v^(2) , v^(2)`
minimize of take the derivative of `(g^(2)d^(2))/v^(2)+v^(2)`
`O=d/(dv)(g^(2)d^(2)/v^(2)+v^(2))=(-2g^(2)d^(2))/v^(2)+2v Rightarrow v^(2) = g^(2)d^(2)=v=sqrt(gd)`
`v=sqrt(10xx10)=10m//s`