The equation of motion of a projectile is `y = ax - bx^(2)`, where a and b are constants of motion. Match the quantities in Column I with the relations in Column II.

Options

A. `A-p, B -q, C-r, D - s `
B. `A-s, B -p, C-q, D - r `
C. `A-s, B -p, C-r, D - q `
D. `A-p, B -s, C-r, D - q `

Answer

C

Explanation

Comparing given equation, `y=ax-bx^(2)` With the equation of projectile motion `y=xtantheta-(gx^(2))/(2u^(2)cos^(2)theta)`
we get, `tantheta=a" ".......(i)`
and `(g)/(2u^(2)cos^(2)theta)=b" "......(ii)`
`:.(gsec^(2)theta)/(2u^(2))=bor(g(1+tan^(2)theta))/(2u^(2))= b`
or `u^(2)=(g(1+tan^(2)theta))/(2b)=" "` (Using(i))
or `u=sqrt([g(1+a^(2))/(2b)]),A-s`
(B) Horizontal range, `R=(u^(2)sin2theta)/(g)=(2u^(2)sinthetacostheta)/(g)`
`R=(2u^(2)cos^(2)theta)/(g)xxtantheta=(a)/(b)" "` (Using (i) and (ii))
B-p
(C) Maximum height, `H=(u^(2)sin^(2)theta)/(2g)`
`H=(u^(2)cos^(2)theta)/(2g)xxtan^(2)theta=(2u^(2)cos^(2)theta)/(4g)xxtan^(2)thet=(a^(2))/(4b)`
`C-r" "` (Using (i) and (ii))
(D) From eqn. (ii),
`u^(2)cos^(2)theta=(g)/(2b)orucostheta=sqrt((g)/(2b))" ".......(iii)`
Time of flight `=(2usintheta)/(g)=(2ucostheta)/(g)xxtantheta" "` (Using (i) and (iii))
D-q