Calculating Velocity & Displacement of a Dropped Object

[Kaxa2000]

A 1 Kg object is dropped from rest from a helicopter at an altitude
of 2000 meters. What is the velocity of the object just before it lands upon a thick bed of pillows? The top of the pillow stack is at zero altitude. If the restoring force
constant (spring constant) of the stack of pillows is 1 N/m, how far into the stack will the
object travel before it comes to a full stop? Neglect air resistance.

 

[CompuChip]

So you can start by calculating the final velocity. There are two ways to go here: one would be to use forces (Newton's laws, etc); and the other is using energies (conversion from potential to kinetic energy, etc).

Since the second part of the question includes a spring, I suggest you are supposed to use energies here?

So there are two relevant points: the point where the object is dropped and the point 2000 meters below it where it hits the pillows. As you know, the total energy
E_total = E_potential + E_kinetic
is conserved (i.e. the same at these two points), where E_potential is the gravitational energy.
Can you give me the formulas for the two quantities on the right hand side and express them in given values and unknowns?

 

[Kaxa2000]

Would it be

mgh + 1/2mv²

(1kg)(9.8m/s²)(2000m) + (1/2)(1kg)(v)²

 

[Kaxa2000]

After you solve for v you get 200 m/s.

Do you set the KE = to the spring equation after that to find distance it goes into pillows?

1/2mv^2 = kX?

 

[denverdoc]

almost--energy in a spring is of the same form=1/2kx^2 As written above you are equating energy and force.