A helicopter on a flood relief mission flying horizontally with a speed u at an altitude `h`, has to drop a food packet for a victim standing on the ground. At what distance form the victim should the food packet be dropped.

Explanation

Refer to fig. 2 (d) .29. O is the position of helicopter from where a food pacet is dropped (B). Be the posotion of victim. The food packet follows a parabolic path while going from ` O to B`.
.
Taking vertical downward motion of food pachet from ` O to B` we have
` u_(y) =0, y_(0) =0, y= H, a_(y) =g, t=?`
As `y=y_(0) +u_(y) + u_(y) + 1/2 a_(y) t^(2)`
:. H=0 +0 + 1/2 gt^(2) a_(y) or t= sqrt(2 H)/g`
Taaking horizontal motion of food packet from ` O to B`, we have
`x_(0)=0, x=x, u_(x) =u, a_(x) =0, t= sqrt (2 H)/g`
As `x =x_(0) + u_(x) +1/2 a_(x)t^(2)`
:. x=0 +u sqrt (2 H)/g + 0 =sqrt (2 u^(2) H)/g`
:. AB=x= sqrt(2 u^(2) H)/g`
distance ` OB= sqrt (OA^(@) + AB^(2))`
`= sqrt H^(2) +(2 u^(2) H)/g`.