Question

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Answer 1

♠ ANSWER :

$１ .\: what \: is \: projectile$

⌛ A PROJECTILE is a name given to any body which once thrown into space with some initial velocity, moves thereafter under the influence of gravity alone without being propelled by any engine or fuel.

⏺️The path followed by a projectile is called its
$trajectory$
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$２. \: examples$

➊. A javelin thrown by an athlete.

➋. An object dropped from an aeroplane.

➌. A bullet fired from a rifle.

➍. A jet of water coming out from the side hole of a vessel.

➎. A stone thrown horizontally from top of a building.

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$３. \: \: show \: that \: the \: path \: of \: projectile \: is \: a \: parabolic \: path \: when \: projected \: horizontally \: from \: a \: certain \: height \:$

⌛ PROOF :
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As shown in figure suppose a body is projected horizontally with initial velocity
$u$
From a point
$o$
at a certain height
$h$
above the ground level. The body is under the influence of two simultaneous independent motions :

⑴ . Uniform horizontal velocity
$u$
⑵ . Vertically downward accelerated motion with constant acceleration
$g$
Under the combined effect of the above two motions, the body moves along the path OPA.

After the time t, Suppose the body reaches the point P ( x, y ).

The horizontal distance covered by the body in time t is

x = u t

t = x / u

The vertical distance travelled by the body in time t is given by

s = u t + 1 / 2 a t²

y = 0 × t + 1 / 2 g t²

y = 1 / 2 g t² [ For vertical motion, u = 0 ].

y = 1 / 2 g ( x / u ) ² = ( g / 2 u² ) x²

[ t = x / u ]

y = k x² [ Here k ( constant) = g / 2 u² ]

As y is a quadratic function of x, so the trajectory of the projectile is a PARABOLA.

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