Question

The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly?

Answer 1

Speed = x/t = 146.61/2 = 73.30 mph

direction y = 22.59° northeast

Explanation:

Given;

The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast;

Resultant distance R = 172 (7° northeast)

Time given to make the trip t = 2 hours

Distance moved by wind during the time dw = 25×2 = 50 miles south east.

Let x represent the distance covered by plane without wind during the time and y the direction;

Resolving into horizontal and vertical component;

horizontal;

x cosy + 50cos45 = 172cos7

xcosy = 172cos7 - 50cos45 .....1

Vertical;

xsiny - 50sin45 = 172sin7

xsiny = 172sin7 + 50sin45 .....2

Divide equation 2 by 1

xsiny/xcosy = (172sin7 + 50sin45)/(172cos7 - 50cos45)

tany = 0.4160

y = taninverse (0.4160)

y = 22.59° northeast

Substituting y into equation 2;

xsin22.59 = 172sin7 + 50sin45

x = (172sin7 + 50sin45)/sin22.59

x = 146.61 miles

Speed = x/t = 146.61/2 = 73.30 miles per hour

Speed = 73.30mph