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

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In summary, the problem involves a plane dropping a bundle of supplies to a castaway on a small raft. Newton's second law is used to determine the bundle's position in flight as a function of time. To hit the raft, the bundle must be dropped a certain distance before it. This distance can be calculated using the given values of initial speed, height, and acceleration due to gravity. To land within ±10m of the raft, the pilot must drop the bundle within a certain time interval, which can be found by considering the effect of a delayed drop on the landing position.
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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





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.
 
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The general solution for c) is extremely simple. Find it.
 
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Bashyboy said:
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?
 

1. What is Newton's second law of motion?

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In simpler terms, the larger the force applied to an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate.

2. How does Newton's second law apply to dropping a package?

When a package is dropped, it experiences a force due to the Earth's gravitational pull. According to Newton's second law, this force will cause the package to accelerate towards the ground. The acceleration of the package will depend on the mass of the package and the force of gravity acting on it.

3. What is the relationship between mass and acceleration in Newton's second law?

As mentioned before, according to Newton's second law, the acceleration of an object is inversely proportional to its mass. This means that the more massive an object is, the less it will accelerate under the same force. This can be seen when comparing the acceleration of a feather and a bowling ball when dropped from the same height.

4. How does the position of the package affect its acceleration?

The position of the package will not affect its acceleration as long as the gravitational force remains constant. This is because the acceleration due to gravity is a constant value (9.8 m/s^2), regardless of the object's position. However, if there are other forces acting on the package, such as air resistance, its position may affect its overall acceleration.

5. What are some real-life applications of Newton's second law?

Newton's second law is used in many practical applications, such as designing vehicles and structures, predicting the motion of objects in space, and understanding how forces affect the human body during activities like sports or accidents. It is also essential in fields like engineering, physics, and astronomy.

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