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Horizontal Projectile
Horizontal Projectile
HORIZONTAL PROJECTILE
Any body projected into the air at an angle other than 90° with the horizontal near the surface of the earth, is called a projectile.
The science of projectile motion is called ballisticsExamples for projectiles:
i) A cricket ball thrown by a fielder
ii) A bullet fired from a gun
iii) A javelin thrown by an athlete
iv) A jet of water from a rubber tube impelled into air -
Horizontal Projectile
HORIZONTAL PROJECTION FROM THE TOP OF A TOWER
Equation for Path (Trajectory):
Suppose a body is projected horizontally with an initial velocity u from the top of a tower of height 'h' at time t=0. As there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion.Hence after time t, the velocity in horizontal direction will be \( v_x = u \).
Let the body reach a point 'P' in time t. Let x and y be the coordinates of the body.
For the y-coordinate, after time t seconds
\( y = \frac{1} {2}gt^2 \) \( [\therefore y = u_y t + \frac{1} {2}a_y t^2 ] \)..............(1)
For x- coordinate, after t seconds
x = ut ( \(\therefore\)the horizontal velocity is constant)
\( \Rightarrow t = x/u \)........(2)
From Eqs. (1) and (2) we get
\( y = \frac{1} {2}g\left( {\frac{x} {u}} \right)^2 \therefore y = \left( {\frac{g} {{2u^2 }}} \right)x^2 \)..........(3)
g and u being constants, \( \left( {\frac{g} {{2u^2 }}} \right) \) is a constant
If \( \left( {\frac{g} {{2u^2 }}} \right) \)=k then y=\( kx^2 \).
This equation represents the equation of a parabola.