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What is a projectile and what are the assumptions made in the study of projectile motion? 


A body projected with some initial velocity and then allowed to fall only under gravity is called a projectile. 

Assumptions made in the study of projectile motion: 

(i) Acceleration due to gravity ‘g’ is constant both in magnitude and direction.

(ii) There is no resistance due to air.

(iii) The earth is flat.

(iv) Rotational motion of the earth is absent.

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An aeroplane is flying in horizontal direction with velocity u at a height h. How far from the target, should the bomb be released from it so as to hit the target?

Let the aeroplane be flying at height h in horizontal direction with velocity u. Let the bomb be dropped from O to hit the target.
Let t be time taken by the bomb to reach the ground at target.

Let the aeroplane be flying at height h in horizontal direction with
We know,      straight y equals straight y subscript straight o plus straight u subscript straight y straight t plus 1 over straight a straight a subscript straight y straight t squared
∴                   straight h equals 0 plus 0 plus 1 half gt squared
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Distance travelled by bomb in horizontal direction in time t is,
           straight x equals straight R equals ut equals straight u square root of fraction numerator 2 straight h over denominator straight g end fraction end root
 Bomb must be dropped at a distance space space straight u square root of fraction numerator 2 straight h over denominator straight g end fraction end root from the target.
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A ball rolls off the top of a staircase with horizontal velocity u. If the height of the step is h and the width is b then at what step the ball hits?

Horizontal velocity = u 

Height of the step = h

Let the ball hit the nth step.

Therefore the ball transverses a horizontal distance of nb and falls vertically by nh.

Equation of trajectory of horizontal projectile,

               


Substituting y = nh and x = nb, we get,

                    


               

                

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A projectile is projected horizontally with velocity u. What will be the velocity of the projectile after time t ?

Let a projectile be projected with velocity u in horizontal direction.

Let a projectile be projected with velocity u in horizontal direction
If straight v subscript straight x space and space straight v subscript straight y are X and Y components of velocity at any instant, then
         straight v subscript straight x equals straight u subscript straight x plus straight a subscript straight x straight t space space space and space space straight v subscript straight y equals straight u subscript straight y plus straight a subscript straight y straight t
space space space space space equals space straight u space space space space space space space space space space space space space space space space space space space space space space space space equals space gt
therefore space space space space straight v with rightwards arrow on top space equals space straight v subscript straight x straight i with hat on top space plus space straight v subscript straight y straight j with hat on top
Now manitude of resultant velocity is,
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and the angle which the velocity vector makes with horizontal is,
                             tanθ equals gt over straight u



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A body is projected with velocity u at angle θ with horizontal. At what instant will it make an angle α with the horizontal?

The instant at which the body will make an angle straight alpha with the horizontal is given by, 

                   

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