Question-46482

Question Number 46482 by peter frank last updated on 27/Oct/18

Commented by peter frank last updated on 27/Oct/18

help

Answered by tanmay.chaudhury50@gmail.com last updated on 28/Oct/18

h o r i z o n t a l v e l o c i t y o f p r o j e c t i o n = v c o s α

v e r t i c a l v e l o c i t y o f p r o j e c t i o n = v s i n α

e q n f o r h o r i g o n t a l m o t i o n

x = (v c o s α) t

e q n f o r v d r t i c a l m o t i o n

y = (v s i n α) t - \frac{1}{2} {g t}^{2}

t h e r e i s n o a c c e l a r t i o n a l o n g h o r i z o n t a l d i r e c t i o n

a c c e l a r a t i o n (g) i s a c t i n g v e r t i c a l l y d o w n

a f t e r t i m e t_{0} t h e v e r t i c a l v e l o c i t y = 0

0 = v s i n α - {g t}_{0} t_{0} = \frac{v s i n α}{g}

t o t a l t i m e o f f l i g h t = 2 t_{0}

= \frac{2 v s i n α}{g}

R a n g e = (v c o s α) (\frac{2 v s i n α}{g}) = v^{2} \times \frac{2 s i n α c o s α}{g} = \frac{v^{2} s i n 2 α}{g}

g r e a t e s t h e i g h t w h e n v e r t i c a l c o m p o n e n t o f

v e l o c i t y i s z e r o .

0^{2} = {(v s i n α)}^{2} - 2 g \boldsymbol H [f o r m u l a v^{2} = u^{2} - 2 a s]

\boldsymbol H = \frac{v^{2} {s i n}^{2} α}{2 g}

y = (v s i n α) t - \frac{1}{2} {g t}^{2}

y = (v s i n α) (\frac{x}{v c o s α}) - \frac{1}{2} g {(\frac{x}{v c o s α})}^{2}

y = x t a n α - \frac{1}{2} g (\frac{x^{2}}{v^{2} {c o s}^{2} α})

y = A x - {B x}^{2}

{B x}^{2} - A x = - y

x^{2} - \frac{A}{B} x = - \frac{y}{B}

x^{2} - 2 . x . \frac{A}{2 B} + \frac{A^{2}}{4 B^{2}} = - \frac{y}{B} + \frac{A^{2}}{4 B^{2}}

{(x - \frac{A}{2 B})}^{2} = (\frac{A^{2} - 4 y B}{4 B^{2}})

{(x - \frac{A}{2 B})}^{2} = (- 4 B) \times \frac{1}{4 B^{2}} (y - \frac{A^{2}}{4 B})

{(x - \frac{A}{2 B})}^{2} = (- 4) \times (\frac{1}{4 B}) (y - \frac{A^{2}}{4 B})

X^{2} = - 4 P Y

f o c u s (0, - P)

x - \frac{A}{2 B} = 0 x = \frac{A}{2 B}

y - \frac{A^{2}}{4 B} = - P

y - \frac{A^{2}}{4 B} = - \frac{1}{4 B}

y = \frac{A^{2} - 1}{4 B}

f o c u s (\frac{A}{2 B}, \frac{A^{2} - 1}{4 B})

d i r e c t r i x Y = P

y - \frac{A^{2}}{4 B} = \frac{1}{4 B}

y = \frac{A^{2} + 1}{4 B}

Commented by peter frank last updated on 28/Oct/18

how do i get focus and directrix

how do i get focus and directrix

Commented by peter frank last updated on 28/Oct/18

God bless you

God bless you