The equation of trajectory followed by a projectile is given by `y =x-(x^(2))/(2)`. At any instant, its x-coordinate is given by `x-(t)/(2)`. At what time (in sec.) does the projectile reach ` y = (1)/(2)m` ?

Options

A. 2
B. 4
C. Never
D. 3

Answer

A

Explanation

`y=x-(x^(2))/(2)" "x=(t)/(2)`
`yimplies(t)/(2)-(t^(2))/(8)`
Put `yimplies1//2`
`implies " "t//2-t^(2)//8=1//2`
`t^(2)-4t+4=0`
`(t-2)^(2)=0`
`t =2`