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Physics Part I

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Class 10 Class 12
A projectile is projected with velocity u at an angle θ with horizontal. Find the time of flight, maximum height attained and horizontal range of projectile.

Let us consider a projectile is projected with velocity u at angle θ with the horizontal direction from a point on the ground.

Let the point of projection be origin, right direction is positive direction of X-axis and vertically upward direction is positive direction of Y-axis. 



Break the components of velocity and acceleration due to gravity in horizontal and vertical direction.

  

Time of flight:

It is the time for which the projectile remains in air above the point of projection. It is represented by T. 

The position of projectile at any instant in Y direction is given by,

space space space space straight y equals straight y subscript straight o plus straight u subscript straight y straight t plus 1 half straight a subscript straight y straight t squared

The time of flight is the difference of instants when the Y position is zero.

i.e.          0 equals straight y subscript straight o plus straight u subscript straight y straight t plus 1 half straight a subscript straight y straight t squared 

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Maximum height:

Maximum height is the greatest height to which the projectile rises above point of projection. It is represented by H.

The displacement of projectile in vertical direction is given by,

                     straight S subscript straight x equals fraction numerator straight v subscript straight y squared minus straight u subscript straight y squared over denominator 2 straight a subscript straight x end fraction

At the highest point, vertical component of velocity is zero.

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Horizontal range:

It is the horizontal distance travelled by the projectile during it's flight. i.e., the horizontal distance travelled covered by object. It is represented by R.

Obviously, it is the distance travelled by projectile in horizontal direction with constant velocity u cosθ in interval equal to time of flight.

i.e.      straight R equals ucosθT equals ucosθ fraction numerator 2 usinθ over denominator straight g end fraction

rightwards double arrow       straight R equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction

 
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