Question

An object is projected with a velocity of `10 m//s` at an angle `45^(@)` with horizontal. The equation of trajectory followed by the projectile is `y = a x - beta x^(2)`, the ratio `alpha//beta` is
A. `5`
B. `10`
C. `15`
D. `20`

Answer 1

Correct Answer - B
`y = alpha x - beta x^(2) = x tan theta - (g x^(2))/(2u^(2) cos^(2) theta)`
`alpha = tan theta, beta = (g)/(2u^(2) cos^(2) theta)`
`(alpha)/(beta) = (tan theta)/(g//2u^(2) cos^(2) theta)`
`= (2u^(2) cos theta sin theta)/(g) = (2u^(2) cos^(2) theta tan theta)/(g)`
`= ((10)^(2))/(10)sin 90^(@) = 10`