Chapter 12, Problem 15CR

To determine

Find the distance between the planes at 2 PM.

Answer to Problem 15CR

C

Explanation of Solution

Given:

Two planes leave the airport at noon, one travelling east at 300 km/h and the other travelling northwest at 450 km/h .

Formula Used:

Law of Cosine :

  $a^2=b^2+c^2-2bc\cos A$

  

Calculation:

Since one plane is going in the East and the other one in Northwest direction, so, the angle between them is $90°+45°=135°$ .

After two hours,

The plane going in east has speed 300 km/h will reach = 300(2) = 600 km

The plane going in northwest has speed 450 km/h will reach = 450(2) = 900 km

Represent the situation and solve :

  

Now, Use Law of Cosine to find c:

  $\begin{array}{l}\Rightarrow c^2={900}^2+{600}^2-2(900)(600)\cos 135°\\ \Rightarrow c\approx 1390.57\end{array}$

So, the distance between them after 2 hours is about 1390.57 km.

So, the correct option is C.