A projectile is fired horizontally with a velocity u. obtain the expression for resultant velocity of the projectile at any instant .

Explanation

At any instant t, at the velocity components of the projectile along both x-axis and y-axis. The resultant of these two components gives the velocity of the projectile at that instant t, as shown in the figure .
The velocity component at any instant of the t along horizontal (x-axis) is `v_(x) = u_(x) + a_(x)t`
Since , `u_(x) = u, a_(x) = 0 ` , we get
`v_(x) = u`
the component of velocity along vertical direction (y-axis) is given by `v_(y) = u_(y) + a_(y) t`
`v_(y) = g t`
`:.` The velocity of the particle at any instant is
`vec(v) = u hat(i) + g t hat(j)`
The speed of the particle at any instant t is given by
`:. v = sqrt(v_(x)^(2)+ v_(y)^(2))`
`v = sqrt(u^(2) + g^(2) t^(2))`