Question

Two bicyclists , starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1080 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1950 m and then.turns and heads directly toward the campground.
(a) At the turning point, how far is the second cyclist from the campground?
(b) What direction (measured relative to due east) must the second cyclist head during the last part of the trip?

Answer 1

Answer:

$DC=1198.6659\ m$

Explanation:

Refer the schematic for explanation.

According to the given condition the first cyclist covers 1080 meters eastwards and then travels 1430 meters northwards to reach the camp.

But the second cyclist travels 1950 meters northwards therefore he travelled 520 meters more in the north than the first cyclist.

So, according to the schematic we find the distance DC in the triangle DCE using Pythagoras theorem:

$DC=\sqrt{1080^2+520^2}$

$DC=1198.6659\ m$