An object is projected with a velocity of `20(m)/(s)` making an angle of `45^@` with horizontal. The equation for the trajectory is `h=Ax-Bx^2` where h is height, x is horizontal distance, A and B are constants. The ratio A:B is (g`=ms^-2)`

Options

A. `1:5`
B. `5:1`
C. `1:40`
D. `40:1`

Answer

D

Explanation

Standard equation of projectile motion
`y = x tan theta - (gx^(2))/(2u^(2) cos^(2)theta)`
Comparing with given equation
`A = tan theta` and `B = (g)/(2u^(2) cos^(2) theta)`
So, `(A)/(B) = (tan theta xx 2u^(2) cos^(2) theta)/(g) = 40`
(As, `theta = 45^(@), u = 20 ms^(-1), g = 10 ms^(-2))`