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Dropping a bundle from a plane: Using Newton's Second Law

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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


Fg = (mgcos(θ),mgsin(θ)) = Fnet



The Attempt at a Solution


mx'' = mgcos(θ)
my'' = mgsin(θ)

Integrating once and dividing out the mass gives...

x' = gcos(θ)*t + Cx
y' = gsin(θ)*t + Cy

I know I need to start from the initial conditions to solve for the constants so I can integrate again... But I don't know where to start and I'm concerned with the best choice of axes to use for this problem. Should I have the x-axis along the path of the bundle or at the ocean?
 

Answers and Replies

  • #2
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Newton's 2nd law,
F=ma.

F/m=dv/dt
v=(F/m)t + c

At t=0, v=v0, then c=v0

ds/dt=(F/m)t + v0

s=0.5(F/m)t2 + v0t + c

Taking at t=0, s=0 then c=0

s=0.5(F/m)t2 + v0t

For download motion, there is gravitational force.
For forward motion, there is no forces acting on it.

So the motions are with directions and magnitude thus they are vectors.
Calculate accordingly with vectors operations.
 
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