Dropping Package Homework: Newton's 2nd Law & Position in Flight

[Bashyboy]

Homework Statement

A plane, which is flying horizontally at a constant speed v0 and at a height h above the sea, must drop a bundle of supplies to a castaway on a small raft

a) Write down Newton's second law for the bundle as it falls from the plane, assuming you can neglect air resistance. Solve your equations to give the bundle's position in flight as a function of time t.

b)How far before the raft (measured horizontally) must the pilot drop the bundle if it is to hit the raft? What is this distance if v0 = 50m/s, h = 100m, and g ≈ 10m/s^2?

c)Within what interval of time (±Δt) must the pilot drop the bundle if it is to land within ±10m of the raft?

Homework Equations

The Attempt at a Solution

I believe I properly solved parts a) and b). For part c), to calculate the time interval, am I suppose to use the specific numerical values given in part b), or am I suppose to derive a general solution? If it is the latter case, can I suppose the separation between the plane and drop-site is d? I am not certain if that would be of much avail, however, for the distance be those two things is constantly shrinking.

 

[voko]

The general solution for c) is extremely simple. Find it.

 

[haruspex]

For part c), to calculate the time interval, am I suppose to use the specific numerical values given in part b), or am I suppose to derive a general solution? If it is the latter case, can I suppose the separation between the plane and drop-site is d? I am not certain if that would be of much avail, however, for the distance be those two things is constantly shrinking.

I agree it's not clear whether you are supposed to use the speed given in part b. Since you are given a specific distance range, I expect you are. You don't need to know the actual separation. All the question is asking is this: if the drop is delayed by Δt how much difference will that make to the landing position?