. 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?

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed =

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 =

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;

= + - 2bcCos A

   = + -2(5000 x 3000) Cos 105

   = + -2(5000 x 3000) x (-0.2588)

   = 2.5 x + 9 x + 7764000

   = 41764000

a =

  = 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

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