Relative Velocity along a Straight Line problem

In summary, a helicopter at 8.50 m above the ground and descending at 3.50 m/s drops a package from rest. The velocity of the package relative to the helicopter is 9.4 m/s downward and the velocity of the helicopter relative to the package is 9.9 m/s upward. Using the kinematic equations, the velocity of the package relative to the ground was found to be 12.9 m/s downward.
  • #1
lauren333
5
0
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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  • #2
I don't know what that equation means.

Are you familiar with "the kinematic equations"?
 
  • #3
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
 
  • #4
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).
 
  • #5
Thank you so much! I will try my best to solve the problem and let you know what I come up with
 
  • #6
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?
 
  • #7
Looks OK. I didn't check the numbers.
 

Related to Relative Velocity along a Straight Line problem

1. What is relative velocity along a straight line?

Relative velocity along a straight line is the measurement of how fast one object is moving relative to another object, in a straight line. It takes into account the velocity and direction of both objects.

2. How do you calculate relative velocity along a straight line?

To calculate relative velocity along a straight line, you must first determine the velocities and directions of the two objects. Then, you can use the formula: relative velocity = velocity of object 1 - velocity of object 2. This will give you the relative velocity along a straight line between the two objects.

3. What is the difference between relative velocity and absolute velocity?

Relative velocity takes into account the motion of one object relative to another object, while absolute velocity is the measurement of an object's speed and direction without considering any other objects. Absolute velocity is constant, while relative velocity can change depending on the motion of other objects.

4. How does distance affect relative velocity along a straight line?

The distance between two objects can affect the relative velocity along a straight line. If the distance between the two objects is decreasing, the relative velocity will increase. If the distance is increasing, the relative velocity will decrease. This is because the closer the objects are, the more their velocities will affect each other.

5. Can relative velocity along a straight line be negative?

Yes, relative velocity along a straight line can be negative. This occurs when the two objects are moving in opposite directions. In this case, one object's velocity will be subtracted from the other object's velocity, resulting in a negative value for the relative velocity.

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