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