Chapter 12.6, Problem 2P

To determine

To determine the distance between planes after 2 hours.

Answer to Problem 2P

Distance between them is approximately 1486 km

Explanation of Solution

Given information :

Plane flying west at a speed of 500 km/h

Plane flying south eas at 300 km/h

Distance travelled by the two planes in 2 hrs.

  $\begin{array}{l}500\times 2=1000\\ 300\times 2=600\end{array}$

According to the direction given the angle between them is ${135}^{\circ }$

  

Here we shall use the cosine formula to determine the length of AB that is the length of lake.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Hence we put the values given,

  $\begin{array}{l}\cos {135}^{\circ }=\frac{{600}^2+{1000}^2-{\left(CB\right)}^2}{2\left(600\right)\left(1000\right)}\\ -848528.13=1360000-{\left(CB\right)}^2\\ {\left(CB\right)}^2=2208528\\ CB=1486\end{array}$