Originally posted by wormer
I need help on solving the following problem: A ball is thrown from a height of 1.6m, at a speed of 11.5m/s and at an angle of elevation of 45.9 degrees. How far from the person who threw it does the ball land?
Whenever you're having trouble with a physics problem, try following these basic steps:
1. Draw a picture of the situation. Make sure you include all the pertinent information (the height of the ball when thrown, the shape of the path the ball will take, a vector indicating the initial speed, the angle at which is was thrown, etc...).
2. Decide which variables and equations are important. If you're stuck, try asking yourself what would change the answer. What would happen if the ball were thrown harder? What about if it were thrown from higher up? What if it were thrown on a steeper angle? A shallower angle? What if it were thrown on the moon? In outer space? By asking yourself these questions, and visualizing the answers, you'll help develop your physical intuition (the thing that lets you know when you've made a mathematical mistake, because the result is unrealistic). Once you've discovered which variables matter, review your basic equations and see which ones contain the variables you're interested in. Then ask yourself if they apply in this case. Do the equations help you determine specific points along the path of a thrown object? Or do they only describe the energy of the projectile?
3. Decide what you're looking for. In this case, you're looking for distance, so find the equation that relates distance to the important variables (your "master equation"
. Determine if there are any variables in the equation that are currently unknown, and if there are try to apply another equation that describes the unknown variable. Keep working backwards like this until you have all the information you need to solve the master equation.
4. Crunch the numbers. If algebra isn't your forte, make sure to calculate one step at a time and write each step out. It make take you an extra minute or two, but the effort will be well worth it when you look back on your solution and see how clear it is.
5. Check your answer. First, ask yourself if the answer seems physically realistic. If you come up with a distance of 2 m (about 6 ft) or 200 m (600 ft), you've probably made a mistake - when's the last time you saw someone throw a ball that short or that far? If you come up with a reasonable answer, try plugging it back into your equations and solving for a given variable (e.g. try plugging in the distance and solving for the initial velocity). If the answers match up, chances are you're doing fine.
6. Answer the question. The easiest way to make sure you've answered the correct question is to paraphrase the original. In this case, the question is "How far from the person who threw it does the ball land?", so an appropriate answer would be something like "The ball landed x m from the person who threw it.". Remember, physics is about predicting and explaining the physical world around us, so words count. The math is simply a tool that serves this ultimate purpose.
Try this method out, and feel free to post your work in progress. Remember, if you get stuck ask for help! Just make sure you've put some thought into the problem and identified a specific stumbling block before you ask, because having someone serve you the answer on a silver platter does you absolutely no good.