Answer:
the rotation rate would be 7.27° per second
Explanation:
we can imagine a triangle formed by the distance walked by the man along the path (L=horizontal side) the vertical distance (H=distance from the path = constant = 20 feet) and the hypotenuse as the searchlight pointing at the man with an Ф angle from the vertical side (rotation angle from the closest point)
when the man is at L1 = 15 feet from the closest point
tg Ф1 = L1/H = → Ф1 = tg ⁻¹ ( L1/H) = tg ⁻¹ ( 15 feet/20 feet ) = 36.869 °
if the man walks at v = 4 feet/s , 0.1 seconds after he would be at
L2= L1 + v* t = 15 feet + 4 feet/s * 0.1 seconds = 15.4 feet from the closest point
then the angle of the searchlight would be
tg Ф2 = L2/H → Ф1 = tg ⁻¹ ( L2/H) = tg ⁻¹ ( 15.4 feet/20 feet ) = 37.596°
therefore when the man covers a distance from 15 feet to 15.4 feet in 0.1 seconds , the rotation angle will vary from 36.869 ° to 37.596° . thus the rotation rate would be:
rotation rate = change of angle / time required for that change = (37.596°-36.869°)/ 0.1 seconds = 7.27° per second