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

The distance between them after 30 minutes is 6.5 km.

Explanation:

Speed =
`(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 =
`√(41764000)`

= 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.