Isn't this statement regarding projectile motion wrong?
If a body is thrown at an angle to the horizontal with initial velocity $u$, then displacement of body as a function of time is $\vec{s}=\vec{u}t+\frac12\vec{g}t^2$. (Air drag is neglected)
How can it be correct? Gravity acts in downward direction, so wouldn't the displacement be $\sqrt{x^2+y^2}$?
Note the vector signs! The vector signs mean that direction is included in the equation. So g only has a y component, but u may have components in any direction.
The equation
$$\vec s = \vec u t + \frac{1}{2}\vec g t^2 $$
is a vector equation and represents three equations (assuming vectors with three components $x, y, z$):
$$s_x = u_x t + \frac{1}{2} g_x t^2$$
$$s_y = u_y t + \frac{1}{2} g_y t^2$$
$$s_z = u_z t + \frac{1}{2} g_z t^2$$
Assuming $\hat z$ is the "up" direction, then
$$g_x = g_y = 0$$
$$g_z = -g$$
