Science Buddies: "Ask an Expert"

I need help on these physics questions because I'm not really sure how to use the velocity/accelearation forumulas. Also, what is downward trajectory. If I could get some pointers, that would be great. Thanks in advance.
#1:You are in charge of a large catapult which is attempting to hurl a large stone up to a castle 15 m above your current location. You set up the catapult a distance x from the edge of a cliff. You know that the stone will be launched with a speed of 40 m/s and at an angle of 45 degrees. At what distance x from the castle should you place the catapult for it to hit the castle on its downward trajectory?

#2: What forces act on a 50 kg block which is being pushed across a frictionless floor (from rest) with a constant force of 10 Newtons at an angle of 30 degrees from the horizontal? What is the order of the strengths and the directions? After being pushed for 10 seconds how fast will the box be travelling? How far will it have traveled?

#3: With what amount of force must a person pull on the vertical portion of a rope to make a 1000 kg refrigerator travel up a 45 degree rough (0.10) plane at constant speed? When the refrigerator just about reaches the top of the inclined plane the rope breaks. With what magnitude of acceleration does the refrigerator accelerate down the ramp?

snowfox

These sound like homework problems. Science Buddies is geared toward helping people with science fair projects and not with homework.

#1. This problem deals with figuring out how high the stone will go before it starts falling. You are given an angle of inclination. From trigonometry or geometry you can determine how much of the 40 m/s velocity is upward velocity and how much is horizontal velocity. Unfortunately, absent the knowlege of the mass of the stone, you can't tell how high it will go before it starts falling. I have no clue why "You set up the catapult a distance of x from the edge of a cliff" was included. Was there some other information given with that as a separate experiment that might provide you with force or mass?

#2. This problem requires you to convert a 10 newton force angled at 30 degress of declination into horizontal and downward forces. That part is a straight forward trigonometry problem. Since the force is constant and the mass is constant and the clasic relationship F = m a is linear, accelleration is constant. You then either need to know integral calculus and plug and chug out the answer or you need to look up the general solution for distance travelled under constant acceleration and plug in the knowns to convert the general solution to the specific solution.

#3. This is a two part question. The first part is subject to a lot of interpretation. What precisely is meant by "the vertical portion of a rope"? If I were a student dealing with this, I would state that this is subject to interpretation and then provide all my assumptions including that the rope was also at 45 degrees (simplest case where the vertical and horizontal force components are equal) and is alligned with a plane that passes through the center of gravity of the refrigerator so that there is no tipping force on the refrigerator.

The second part is only a slightly better defined problem. You again have to make an asumption about whether the refrigerator tips over or not. The easiest case is to state your assumption that the center of gravity is low enough so that the refrigerator stays at a 45 degree angle until it reaches the bottom of the ramp where it tips over. For that case, you can state that the horiozontal accelleration is less than or equal to the gravitational constant. This makes the accelleration down the ramp (45 degree angle of declination) between the gravitational constant and 1.414 times the gravitational constant.

Where are these problems coming from? I hope they were intentionally vague to get you to think about the underlying physics principles and not as plug and chug exercises. If they are the latter, then the originator of the problems doesn't understand the subject or something got lost in the translation/transcription.