Question

03.3 You fly an airplane to a city that is 800 miles to the west and 300 miles to the north of your starting point. The wind is blowing from east to west. Your plane has an air speed of 200 mph and the trip takes 3.55 hours. a) In what direction did you aim the plane? b) What is the speed of the wind?

Answer 1

a)

using pythagorean theorem

AC = sqrt(AB² + BC²) = sqrt(800² + 300²) = 854.4 miles

also ,

= tan^-1(BC/AB) = tan^-1(300/800) = 20.6 deg

t = time = 3.55 h

consider the motion along the north direction

V_py = component of velocity along north direction = ?

D_y = distance in north direction = 300 miles

t = time taken = 3.55 h

using the equation

t = D_y /V_py

3.55 = 300/V_py

V_py = 84.5 mph

consider motion along the west direction

D_x = distance along west direction = 800 miles

t = time = 3.55 h

V_p = plane speed = 200 mph

using pythagorean theorem

V_px = sqrt(V_p² - V_py²) = sqrt((200)² - (84.5)²) = 181.3 mph

V_w = speed of wind = ?

using the equation

t = D_x /(V_px + V_w)

3.55 = 800/(181.3 + V_w)

V_w = 44.1 mph

= direction = tan^-1(V_py/V_px) = tan^-1(84.5/181.3) = 25 deg north of west