38 - Rate of rotation of search light pointing to a ship

$\theta = \arctan \dfrac{8(t - 0.5)}{4}$

$\theta = \arctan 2(t - 0.5)$

$\dfrac{d\theta}{dt} = \dfrac{2}{1 + 4(t - 0.5)^2}$
 

after t = 2 hrs
$\dfrac{d\theta}{dt} = \dfrac{2}{1 + 4(2 - 0.5)^2}$

$\dfrac{d\theta}{dt} = \dfrac{2}{1 + 4(2.25)}$

$\dfrac{d\theta}{dt} = 0.2 \, \text{ rad/hr}$           answer