Answer to Question #219883 in Mechanics | Relativity for Fheyy

Question

A border patrol helicopter set out to catch a drug smuggler on a speed boat. The speed
boat is travelling south of manila going 27m/sec and left 2 hours ago. If the helicopter
leaves now and travel 67 m/sec. how long will it take to catch the smuggler.

Answer 1

The initial distance between boat and helicopter

$$d=v_b*\Delta t=(27\:\rm m/s)*2*3600\: s=194400\: m$$

The time needed for a border patrol to catch the smuggler

$$t=\frac{d}{v_{rel}}=\frac{d}{v_h-v_b}\\ =\frac{194400\:\rm m}{(67-27)\:\rm m/s}=4860\: \rm s=81\: min=1.35 \: hr$$