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3 years ago

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A plane flying against the wind covers the 900-kilometer distance between two aerodromes in 2 hours. The same plane flying with

the wind covers the same distance in 1 hour and 48 minutes. If the speed of the wind is constant, what is the speed of the wind?

1 answer:

Mashcka [7]3 years ago

4 0

Answer:

The speed of the wind is 25 km/hr.

Explanation:

Let us call $v_p$ the speed of the plane and $v_w$ the speed of the wind. When the plane is flying against the wind, it covers the distance of 900-km in 2 hours (120 minutes); therefore;

(1). $v_p - v_w = \dfrac{900km}{120min}$

And when the plane is flying with the wind, it covers the same distance in 1 hour 48 minutes (108 minutes)

(2). $v_p+v_w= \dfrac{900km}{108min}$

From equation (1) we solve for $v_p$ and get:

$v_p = \dfrac{900km}{120min}+v_w$ ,

and by putting this into equation (2) we get:

$\dfrac{900km}{120min}+v_w+v_w= \dfrac{900km}{108min}$

$2v_w= \dfrac{900km}{108min}-\dfrac{900km}{120min}$

$2v_w = 8.3km/min - 7.5km/min$

$2v_w = 0.83km/min$

$v_w = 0.4165km/min$

or in km/hr this is

$\boxed{v_w= 25km/hr }$

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<h2>a) </h2>

We know that the cross product of linearly independent vectors $\vec{A}$ and $\vec{B}$ gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.

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<h2>B)</h2>

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Therefore, correct option is

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