A pair of hikers sets off from their cabin and travels 1.97 km due North. After
ID: 1591843 • Letter: A
Question
A pair of hikers sets off from their cabin and travels 1.97 km due North. After stopping for lunch, they travel 1.20 km in a direction 28.0° South of East. They then travel 0.666 km due East before stopping for a snack. Draw a diagram representing their travels and answer the following questions.
How far East of the cabin did the hikers travel before stopping for a snack?
How far North of the cabin did the hikers travel before stopping for a snack?
Their friends who stayed back at the cabin now want to join them. What is the shortest distance they need to walk in order to get to the point where the original hikers are eating their snack?
Expressed as an angle North of East, what direction do the new hikers need to travel in order to get to the original hikers by traveling in a straight line? (Use 'deg' to represent units of degrees.)
Explanation / Answer
a)
Distance due east = bc + 0.836 km
Distance = 1.2 cos 28 + 0.666
Distance towards east = 1.725 km (answer)
b)
distance due North = 1.97 - 1b
=2.62 - 1.2sin 28
Dn towards north = 2.056 km (answer)
c)
distance due North = 1.725 km
distance due east = 2.056km
shortest distance = sqrt (1.725^2 + 2.056^2) = 2.683 km (answer)
d)
tan theta a = Dn/De
tan theta = atan (1.725/2.056)
theta = 40 deg
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.