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Example Projectile Motion

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Example Projectile Motion

1. 1. Few Guidelines <ul><li>Please sit with your pen and paper as you go through this power point show. </li></ul><ul><li>Follow the instructions provided in the slides for maximum learning of the concepts. </li></ul><ul><li>Lets Start !!! </li></ul>
2. 2. Problem Statement <ul><li>A ball is thrown at a certain angle α from base of a incline with an inclination β . The initial speed of the ball is u. The ball hits the inclined surface perpendicularly as it lands back on the incline. Find : </li></ul><ul><li>The time for which the ball was in air. </li></ul><ul><li>The distance traversed by the ball along the incline. </li></ul>
3. 3. Instructions <ul><li>Try to visualize the problem as the picture in the problem is not provided. </li></ul><ul><li>Correct visualization of the problem is half the job done. </li></ul><ul><li>Don’t click on the next slide before you finish the pictorial representation of the problem statement. </li></ul><ul><li>Click for next to see the picture drawn by you matches with the given picture in the slides. </li></ul>
4. 4. Pictorial Representation u β α INCLINE L Have to get (i) Time of flight (T) (ii) Value of L
5. 5. Instructions <ul><li>Those students who got their pictures right have 25% done with the problem as they know what to do. </li></ul><ul><li>The main concern is how to do !!! </li></ul><ul><li>Those students who did not got their pictures right , please go back and read the question again for two-three times and try to visualize it and draw it again. </li></ul>
6. 6. Solution <ul><li>The first step to solve a problem of this kind must involve a co-ordinate axis selection. </li></ul><ul><li>A lot of students I have seen select the co- ordinates as shown on the picture on the next slide. </li></ul>
7. 7. Axis Selection u β α INCLINE Y X
8. 8. This is not a smart selection <ul><li>The selection of such co ordinates is not a smart selection as the solution will consume a lot of tedious calculations. </li></ul><ul><li>Why don’t we think something out of the box !!! </li></ul><ul><li>What if a new type of co-ordinate axis is selected as shown in the picture on the next slide. </li></ul>
9. 9. Axis Selection (Intelligent) u β α INCLINE Y X
10. 10. How this is smart !!! <ul><li>Now we will have a look on how this subjective looking question can be solved in few lines like an objective multiple choice question. </li></ul><ul><li>For Step 2 we will decide the accelerations along the X axis and Y axis. </li></ul>
11. 11. Acceleration along the axes u β α INCLINE Y X g β g Cos β g Sin β
12. 12. Instruction <ul><li>Always indicate accelerations in the diagram using dotted lines. (Many students never draw it ending up with unclear diagrams) </li></ul><ul><li>You will never confuse the other lines with the acceleration lines in the picture drawn by you. </li></ul><ul><li>This will minimize the chance of mistake by you. </li></ul>
13. 13. Data Collected till now <ul><li>As it is very much clear by the picture that </li></ul><ul><li>Acceleration along X axis = -g Sin β . </li></ul><ul><li>Acceleration along Y axis = -g Cos β . </li></ul><ul><li>Initial Velocity along X axis = u Cos α . </li></ul><ul><li>Initial Velocity along Y axis = u Sin α . </li></ul><ul><li>Final Velocity along X axis = 0.(How !!!) </li></ul><ul><li>Please think how the final velocity along Y axis is zero before going on next slide. </li></ul>
14. 14. u β α INCLINE Y X g β g Cos β g Sin β As mentioned in the problem the ball strikes the inclined surface perpendicularly. So its velocity along X axis is zero. Have a look on the picture and get it concept cleared.
15. 15. Formula to be used !!! <ul><li>v = u + at </li></ul><ul><li>v 2 – u 2 = 2as </li></ul><ul><li>Now applying the first formula along the X axis to get the time of flight !!! </li></ul>
16. 16. <ul><li>v x = u x + a x t </li></ul><ul><li>Substituting the values we have, </li></ul><ul><li>0 = u Cos α - g Sin β × t </li></ul><ul><li>or, time of flight (t) = u Cos α / g Sin β </li></ul><ul><li>Answer for first sub question : </li></ul><ul><li>Time of Flight = u Cos α / g Sin β </li></ul>Solution Steps
17. 17. Instruction <ul><li>Solve this question using the Axis selection as shown on slide number 7. </li></ul><ul><li>Match the answer as calculated in the previous slide. </li></ul><ul><li>After solving the question by the above mentioned axis selection , you will realize the value for this smart axis selection. You got your answer in a single line by this method. </li></ul>
18. 18. Solution Steps Continued : <ul><li>Now to calculate the value of L we use the second formula along the X axis. </li></ul><ul><li>v 2 x – u 2 x = 2a x L </li></ul><ul><li>or, 0 – ( u Cos α ) 2 = 2 (-g Sin β ) L </li></ul><ul><li>or, L = u 2 Cos 2 α / 2g Sin β . </li></ul>The distance traversed by the ball along the incline = u 2 Cos 2 α / 2g Sin β
19. 19. Instructions <ul><li>You can choose the Axis smartly from now onwards for questions on similar lines. </li></ul><ul><li>Be cautious if you are adopting a new style of problem solving as your concepts must be crystal clear before applying it on some problems </li></ul><ul><li>Short-Cut helps only if your concepts are clear !!! </li></ul>
20. 20. For Future Correspondence <ul><li>For any assistance, feel free to contact me on 9920685139. </li></ul><ul><li>You can always contact me at www.vidyacenter.com </li></ul><ul><li>You can write me at [email_address] </li></ul>
21. 21. Thank You