Question

Suppose, a lighthouse operator (L) observes a shipping boat (B) that is moving straight away from the light house. The level of the lighthouse operator is 20 m above the level of the sea. At a particular instant, the lighthouse operator observe the boat (B1) with a depression angle of 400. Two minutes later, the boat (B2) was observed with a depression angle of 800.
• What is vB, the speed of the boat as measured by the light house operator in m/s?
(You can use speed = distance relation to determine the speed.) time
2

Answer 1

$$d_1=h\tan{40\degree}$$

$$d_2=h\tan{80\degree}$$

The speed of the boat as measured by the light house operator:

$$v_B=\frac{d_2-d_1}{t}=\frac{h(\tan{80\degree}-\tan{40\degree})}{t}$$

$$v_B=\frac{20(\tan{80\degree}-\tan{40\degree})}{2(60)}=0.8\frac{m}{s}$$