What should be the expression for the horizontal distance dx at which you release the relief package so that it will arrive to the survivors at the right place? (Neglect the effect of air resistance)

n a relief operation mission involving a helicopter h distance above the ground traveling with a horizontal velocity v_x. What should be the expression for the horizontal distance d_x at which you release the relief package so that it will arrive to the survivors at the right place? (Neglect the effect of air resistance)

Solution

To determine this, we must first derive the time it takes for the relief package to reach the survivors. We use this equation

-h = v_initial-yt + (1/2)a_y

If we just drop the package from the helicopter, the equation above becomes

 =  + (1/2)a_y

Substituting a_y = -g then simplifying results to

t = sqrt( / )

which is the time it takes for the object to reach the ground.

Since the package will just travel at a constant velocity in the x-axis, thus

d_x = v_xt

Substituting the time taken by the package to reach to ground results to:

d_x = (  )( sqrt ( / ) )

which is the expression for the horizontal distance at which you should drop the package.