A particle is thrown with speed `u` at an angle of projection `theta` with horizontal as shown.

(i) The avergae velocity of particle from `O` to `A` is `u cos theta`
(ii) The average velocity of particle from `O` to `H` (highest point) is `(u)/(2) sqrt(1 + 3 cos^(2) theta)`
(iii) The average velocity of particle from `J` to `K` is `u cos theta`
(iv) The angle between the velocity and the acceleration between `O` and `H` is greater than `90^(@)`, between `H` to `A` is less than `90^(@)` and at highest point is `90^(@)`

Options

A. (i), (ii)
B. (i), (iii)
C. (ii), (iv)
D. all option are correct

Answer

D

Explanation

(i) `O` to `A`: `bar(v_(y)) = 0, bar(v_(x)) = ucostheta, bar(v) = u cos theta`
(ii)
`bar(v_(x)) = u cos theta, v_(y) = (u sin theta + 0)/(2) = (u sin theta)/(2)`
`bar(v) = sqrt(bar(v_(x))^(2) + bar(v_(y))^(2)) = sqrt((u cos^(2) theta)^(2) + ((u sin theta)/(2))^(2))`
`= (u)/(2) sqrt(4 cos^(2) theta + sin^(2) theta) = (u)/(2)sqrt(1 + 3 cos^(2) theta)`
(iii) `J` to `K`: `vec(v_(y)) = 0, bar(v_(x)) = u cos theta, bar(v) = u cos theta`
(iv)
`theta`: angle between velocity and acceleration.