In: Physics
SCENERIO: You are working for a humanitarian aid agency that plans to air-drop supplies into a war-torn region. The political landscape is such that in order to reach the civilians in need – and not fall into the wrong hands – the supplies must land in a very precise location. The agency’s helicopters are equipped with a ramp down which bundles of supplies can be rolled as a means of launching them. The bundles of supplies are spherical and cylindrical, and come in a variety of sizes and masses. Enough friction is present on the ramp that all bundles are certain to roll without slipping as they are launched. It is up to you to determine from where on the ramp each bundle of supplies should be launched, assuming the helicopter hovers at a constant height.
QUESTION: Now assume that conditions in the war-torn region have deteriorated to the point that it is no longer safe for a helicopter to hover stationary above the ground for a supply drop. How would your answers about where to drop supplies change if they are instead released from an aircraft moving with constant velocity? With constant acceleration?
Since the helicopters are moving at a constant height, they only have horizontal velocity.
For constant Velocity
A parcel dropped from the helicopter will have the same horizontal velocity, and zero initial vertical velocity.
As it falls, it accelerates with a vertical acceleration equal to the acceleration due to gravity.
At any point during its downward journey, its directly below the aircraft.
The point of drop is decided by dropping in such a way that the time it takes to fall down is the same as the time it takes for the aircraft to reach above the drop point. This is because the aircraft and parcel have the same vertical velocity.
As such, the parcel reaches the ground and the drop site at exact same time.
For constant Acceleration
The parcel will have the same velocity as the aircraft at the instant it was released. It will not have any additional acceleration because there is no force acting on it.
The parcel will be behind the plane at all points in the journey and the aircraft will reach the drop point before the parcel.