Relative Velocity along a Straight Line problem

AI Thread Summary
A helicopter drops a package from 8.50 m above the ground while descending at 3.50 m/s. The problem involves calculating the velocity of the package relative to the helicopter and vice versa, using the relative velocity equation. The correct answers are 9.9 m/s downward for the package's velocity relative to the helicopter and 9.9 m/s upward for the helicopter's velocity relative to the package. The discussion highlights the use of kinematic equations to solve for the package's velocity relative to the ground and emphasizes the importance of applying the right equations for non-constant acceleration scenarios. The participant is encouraged to verify calculations and ensure the correct application of the equations.
lauren333
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1. Homework Statement

A helicopter 8.50 m above the ground and descending at 3.50 m/s drops a package from rest (relative to the helicopter). Just as it hits the ground, find a) the velocity of the package relative to the helicopter and b) the velocity of the helicopter relative to the package. The package falls freely.

2. Homework Equations : package: p , helicopter:h, ground:g
Vp/h = Vp/g + Vg/h (I think this equation might help, but I was unable to successfully solve the problem).

3. Answer: a) 9.9 m/s downward b) 9.9 m/s upward

Thank you! I greatly appreciate your help in solving this problem! :)
 
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I don't know what that equation means.

Are you familiar with "the kinematic equations"?
 
Yes I am, but I don't know what equation to apply to this problem to solve it. The equation I gave was listed in my textbook as a way to solve relative velocity problems:

velocity of the package relative to the helicopter = (velocity of the package relative to the ground) + (velocity of the ground relative to the helicopter)

Note: velocity of the ground refers to velocity of the earth
 
Ah, OK, now I know what your equation means. You will need it, but you will also need (at least) one more kinematical equation. Think about what variables in the equations you know and which ones you're trying to find. Also make sure that the equation that you use is applicable to the situation (e.g. if the acceleration is nonzero, then discard all equations that assume constant velocity).
 
Thank you so much! I will try my best to solve the problem and let you know what I come up with
 
My answer to part a)

Ok, I used the kinematical equation Vy^2 = Voy^2 + 2ay(y-yo) to find the velocity of the package relative to the ground and I got 12.9 m/s downward (or -12.9m/s). I plugged this value into my equation as Vp/g. I know that the velocity of the helicopter relative to the ground (Vh/g) is 3.50m/s downward (or -3.50 m/s). So Vg/h, which equals -Vh/g, is +3.50 m/s. I then solved for Vp/h, and got 9.4 m/s downward...not quite 9.9m/s...did I solve the problem correctly?
 
Looks OK. I didn't check the numbers.
 
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