Sep
27

# PreAP HW: Linear Motion 3 #23 & 24 + answers to questions from notes

PreAP HW and Review items for Linear Motion test:

HW #’s 23 & 24

23. A helicopter is rising at X m/s when a bag is dropped from it.

(a) After Y s, what is the bag’s velocity?

(b) How far has the bag fallen?

(c) How far below the helicopter is the bag?

24. A helicopter descends at A m/s when a bag is dropped from it.

(a) After B s, what is the bag’s velocity?

(b) How far has the bag fallen?

(c) How far below the helicopter is the bag?

OK, so these are basically the same problem.  In each problem you know the same information at the beginning.  Since everybody has different numbers I have given variables in the problems here.  For each problem you know:

a = 9.81 m/s^2 down, t and Vo.  In 23 you will want to make your initial velocity positive while the acceleration of gravity is negative.  This means the bag keeps rising for a bit as a result of its inertia but eventually changes direction and falls. In 24 you will want to make everything positive since everything (displacement, velocity, acceleration) is in the downwards direction.

Use the definition of acceleration (a=(delta)V/t) to find the final velocity for both questions part a).  Remember that delta = final – initial.  Your sign changes are very important in this problem!  Your answer may be positive or negative depending on the initial velocity YOU have been given by webassign.  Postive would mean it is still going ___________, but negative means it is going _________.

On part b) I suggest using x=Vot + .5at^2.  In 23 make sure you put in a positive initial velocity and a negative acceleration.  Since x s the displacement this positive and negative discrepancy will take care of the up/down issue and just give you the position of the bag (i.e., “how far it has fallen”) in your result.  If the bag is on its way down (see note from part a) and has fallen past the starting point you will get a negative answer.  The question asked “how far.” This means it wants the absolute value.  In 24 this point is moot since everything is going downward already.  What you get is what you are looking for.

Part c)  These are really your challenge problems on this assignment.  I will give you a big hint, but I am not going to explain completely.  You have two motions here: The helicopter moving at a constant speed (given in your problem), and the falling bag, accelerating due to gravity.  You already know how far the bag has fallen relative to where it started (answer b).  You must find how far the helicopter has gone either up or down (in #23 or 24 respectively) using constant velocity and either add to or subtract from your value from b.  Which one you do depends on the direction of motion.  Draw a before and after picture for each if you are having a hard time seeing it.  Good luck.

Answers to practice questions at end of notes:

1. Done in class.
2. A) 23.5 m/s         B) 23.6 m/s
3. 29.7 m/s
4. Done in class