# Math Help - Plane type of question

1. ## Plane type of question

Hello, this question is from Grade 12 Calculus and Vectors book.

A pilot in an airplane with an airspeed of 1000 km/hr wishes to fly to a city 2000km due east. There is a wind blowing from bearing of $025^\circ
$
at a speed of 100 km/hr. In what heading should the pilot seer

B) What will be the ground speed of the plane

C) How long will this trip take

2. Originally Posted by daunder
Hello, this question is from Grade 12 Calculus and Vectors book.

A pilot in an airplane with an airspeed of 1000 km/hr wishes to fly to a city 2000km due east. There is a wind blowing from bearing of $025^\circ
$
at a speed of 100 km/hr. In what heading should the pilot seer

B) What will be the ground speed of the plane

C) How long will this trip take
wind blowing from a $025^{\circ}$ bearing is blowing toward $-115^{\circ}$ relative to East.

let $\theta$ be the airplane's heading relative to East.

desire the resultant velocity in the y direction (North-South) to be 0 so the plane will track due East ...

North component of plane's velocity + South component of wind's velocity = 0

$1000\sin{\theta} + 100\sin(-115) = 0$

$\sin{\theta} = \frac{\sin(115)}{10}$

$\theta \approx 5.2^{\circ}$

groundspeed = $1000\cos(5.2) + 100\cos(-115) \approx 954$ km/hr

$t = \frac{2000}{1000\cos(5.2) + 100\cos(-115)} \approx 2.1$ hrs