The horizontal range (R ) of a projectile becomes (R + 2 H) from `R` due to a wind in horizontal direction. Here `H` is the maximum height reached by the projectile. What constant horizontal acceleration is imparted by the wind ?

Explanation

In case of projectile without wind effect, we have
Time of flight, `T = (2 u_y)/(g)`, maximum height reached by a projectile `H = (u_y^2)/(2 g)` and range of a projectile `R = u_x T`.
Due to horizontal acceleration of wind, `T and H` will not change as `u_y` is the only term that appears. If we include the effect of wind the range of the projectile will change. New range will become
`R' = u_x T+ (1)/(2) a T^2 = R + (1)/(2) a((4 u_y^2)/(g^2))`
`R' = R + (4 a)/(g)((u_y^2)/(2 g)) = R + (4 a)/(g) H` ...(i)
But we have given the new range with wind effect
`R' = R + 2 H`..(ii)
Comparing (i) and (ii) we get, `(4 a)/(g) = 2 rArr a = (g)/(2)`.