A small plane is flying north in calm air at 250 mph when it encounters a horizontal crosswind blowingnortheast at 40 mph and a 25-mph downdraft. Find the resulting direction and speed of the ground with respect tothe ground.1.

Given data The plane is flying north in calm air at 250 mph. Speed of the horizontal crosswind…

Answered: A small plane is flying north in calm…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 28E

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Question

A small plane is flying north in calm air at 250 mph when it encounters a horizontal crosswind blowing
northeast at 40 mph and a 25-mph downdraft. Find the resulting direction and speed of the ground with respect to
the ground.
1.

Expert Solution

Step 1

Given data

The plane is flying north in calm air at 250 mph.
Speed of the horizontal crosswind blowing northeast is 40 mph
Speed of the downdraft is 25 mph

The formula to find the position vector that represents the velocity of the plane relative to the ground is,

$v_{g} = v_{a} + w + d \dots (1)$

where,

$v_{a}$ is the velocity of the plane in calm air
$v_{g}$ is he velocity relative to the ground
$w$ is the velocity of the crosswind
$d$ is the velocity of the downdraft wind

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A small plane is flying north in calm air at 250 mph when it encounters a horizontal crosswind blowing northeast at 40 mph and a 25-mph downdraft. Find the resulting direction and speed of the ground with respect to the ground. 1.