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# 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