Question

. Two bicyclists, Sarah and Emily, depart from the same location. Sarah heads N55°E at an average speed of 6 km/hr. Emily heads S20°E at an average speed of 10 km/hr. What is the distance between them after 30minutes?

Answer 1

Answer:

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed = $\frac{distance}{time}$

Sarah's speed = 6 km/hr = 1.6667 m/s

Emily's speed = 10 km/hr = 2.7778 m/s

The measure of angle between their bearings = $105^{o}$

After 30 minutes (1800 seconds);

distance = speed x time

Sarah would have covered a distance = 1.6667 x 1800

                               = 3000 m

                               = 3 km

Emily would have covered a distance = 2.7778 x 1800

                               = 5000 m

                               = 5 km

The distance between them, a, can be determined by applying the cosine rule;

$a^{2}$ = $b^{2}$ + $c^{2}$ - 2bcCos A

   = $5000^{2}$ + $3000^{2}$ -2(5000 x 3000) Cos 105

   = $5000^{2}$ + $3000^{2}$ -2(5000 x 3000) x (-0.2588)

   = 2.5 x $10^{7}$ + 9 x $10^{6}$ + 7764000

   = 41764000

a = $\sqrt{41764000}$

  = 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.