**#18 & 19:**

As discussed in some periods, webassign may score you incorrectly when you try to find the slopes and values of the graphs as indicated in the questions. Eyeball it to the best of your ability and make sure you know HOW to answer the questions, but I will ensure that you receive credit for items like that that webassign marks incorrect that you actually have right.

**#5:**

This problem is a common issue for students because (if you read carefully) you will notice that you have two distinct motions represented here. The knee-jerk approach to this problem is to list out your variables and try to stuff numbers into an equation. This one is not that easy. You actually have two separate physics problems here: one is constant velocity motion, one is accelerated (slowing down) motion.

Your final answer to the question must add the distance the car travels during both time periods, so you first need to find those distances.

Constant Velocity part

If an object is moving at a constant speed, only 1 of our kinematics equations describes its motion: the defn. of velocity–V=(delta)x/t

Based on the information provided in the problem this should be simple to solve for the distance traveled during the reaction time.

Accelerated part

Since this is not constant velocity, the equation we used above goes out the window. You CANNOT use it because it does not account for the acceleration of the car. What this does mean, however, is that you can use any of the other 3 equations, provided you have the requisite information. Here’s what we know:

x = ? Vo = same speed as first part, since you have not yet started braking V = 0 (zero, you have come to a stop)

a = given in problem t = unknown

There are several ways to approach this solution. You can go directly to the displacement (x) if you select the “right” euqation, but you could also find the time first, then use that information to find the displacement. It makes no difference. One important point of caution: Your acceleration opposes the velocity, so you must make sure it is _________?____________

If you answered “negative” you get a cookie.

Don’t forget to add the 2 distances from the 2 parts of the problem when you finish.

**#7:**

I encourage you to approach this question as two separate motions (in some ways similar to number 5, above). While it can be done as an entire trip (up and then down) it may be easier for you to think about it in two parts. Use the information provided to find the height to which the ball goes up–don’t forget to account for the fact that gravitational acceleration is down. Then use the total height to find the impact speed when it falls all the way back to the ground.

Now, on the way down something interesting happens with your problem solving. If you work this from the max height to the ground then your

displacement is ____?____

velocity is ____?____

acceleration is ____?____

Since everything is negative (you did answer negative or downward for all of those items, right?), you might say that concerns about direction cancel out…they really sort of do mathematically. In any event you can solve this using positive numbers provided you recognize that your final answer is downward. This is important because of the way the question is asked in the problem. your final answer for your

velocity is ____?____

speed is ____?____

and since the question asks “how fast” your answer should probably be speed.

**Number 8 is your challenge problem for this assignment.**

This is the one problem I will not help you complete fully, but I will give you the following hint: You need to draw a picture and set up two separate equations for the displacement of the truck (constant velocity) and the displacement of the car (slowing down so need the equation with acceleration). Write one of the displacements in terms of the other (i.e., 500 – x). Both of your equations will be missing a displacement and time term. Solve for time (when they meet the same amount of time must have elapsed). You will have to either graph it or use the quadratic formula. Use time to solve for displacement.

Last hint: Because the car is slowing down fairly rapidly, it will travel the lesser distance. This may help you narrow down your answer.

If you miss it, don’t worry about the points. I always factor some participation points into your grades that will offset these type of challenge problems

Good luck.

**HW #’s 33 & 34 (and notes about 35)**

33. 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?

34. 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.

For question 35, the scenario is the same as 34, but since the helo is descending the initial velocity of the bag will be downward (negative) along with the acceleration of gravity and the displacement (all negative). Like part of #7, above, you can drop these negative signs (or keep them as you wish) since all aspects of your motion are down, in the same direction. Again, take care with part a to ensure that your answer is reflective of direction (down or negative) since the problem specifically asks for “velocity.”