Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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 !!!

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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 :

(i) The time for which the ball was in air.

(ii) The distance traversed by the ball along the incline.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Pictorial Representation

u β

α

INCLINE

L

Have to get

(i) Time of flight (T)

(ii) Value of L

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Axis Selection

u β

α

INCLINE

Y

X

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Axis Selection (Intelligent)

u

β

α

INCLINE

Y

X

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Acceleration along the axes

u

β

α

INCLINE

Y

X

g

βg Cos β

g Sin β

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Data Collected till nowAs 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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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u

β

α

INCLINE

Y

X

g

βg 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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Formula to be used !!!

• v = u + at

• v2 – u2 = 2as

Now applying the first formula along the X axis to get the time of flight !!!

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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• vx = ux + axt

• 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

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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.

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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Solution Steps Continued :

• Now to calculate the value of L we use the second formula along the X axis.

• v2x – u2

x = 2ax L

or, 0 – (u Cos α)2 = 2 (-g Sin β) L

or, L = u2 Cos2 α / 2g Sin β.

The distance traversed by the ball along the incline = u2 Cos2 α / 2g Sin β

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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 !!!

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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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 sinha.gautam@gmail.com

Prepared by : GAUTAM SINHA, B.Tech IIT Kharagpur (2007)

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