Question

A projectile is fired with velocity 'u' making an angle 'o'
with the horizontal. Show that its path is parabolic. Also, find the expressions for :
(1) Maximum height attained
(ii) Time of flight.​

Answer 1

let's solve it baby

taking velocities component

we get

$u \sin(o) in \: y \: axis \\ and \: u \cos(o) in \: x \: axis$

using x axis

$x = ut + 1 \div 2at {}^{2}$

$x = u \cos \: o \: t + 1 \div 2(0)t {}^{2}$

a=0 beacuse there is no acc in horizontal direction

x= u cos o.t -. ------------ 1

using y axis

$y = u \sin \: o \: t \: + 1 \div 2gt {}^{2}$

using 1

$t = x \div ucoso$

$y = u \sin \: o \times x \div u \cos(o ) \\ + 1 \div 2g \times (x \div u \cos(o) ) {}^{2}$

y

$y = xusino \div ucoso \: + 1 \div 2gx { }^{2} \div (ucoso) {}^{2}$

now since sino,coso,1,2and g are constant therefore

$y = x m + kx {}^{2}$

where m= usino/ucoso

$and \: k = 1 \div 2g \div (u \cos(o) ) {}^{2}$

hence acc to equation

[tex]y = xm + kx {}^{2} [/tex

the trajectory is PARABOLIC