A projectile is launched from the surface of the earth with an...

Let the angle of projection with respect to the vertical be $\phi$.

The horizontal component of the initial velocity is $u \sin \phi$.

During projectile motion, the horizontal component of velocity remains constant. At the highest point of the trajectory, the vertical component of velocity is zero, so the speed of the projectile is purely horizontal.

Speed at the highest point $= u \sin \phi$

Given that the speed at the highest point is $\dfrac{u}{2}$, we have:

$u \sin \phi = \dfrac{u}{2}$

$\sin \phi = \dfrac{1}{2}$

$\phi = 30^\circ$

Answer: $30^\circ$