maths

posted by Tammy

A party of bush walkers have an average speed of 50km/minute and walk for 4 hours on a bearing of 231°T. they then walk for 6(1)/(3) hours on a bearing of 117°T. Find a.How far are they from bas e camp?
b. The bearing they must travel along to get to base camp

  1. MathMate

    I assume the speed of the adventurers are 50 m/min. since 50km/min is almost the speed of a supersonic jet.

    Also, not clear about the 6(1)/(3) hours. I take it at face value of 2 hours.

    The bearing of 231°T will be assumed to be measured from true north, clockwise, equivalent to "azimuth" used in US and French speaking countries.

    The solution here lies in the resolution of all distances travelled to directions east (x-axis) and north (y-axis). The components can then be summed together to get the final destination and direction, if required.

    There is a little problem combining bearings and trigonometry, the latter measures angles from zero in the east direction counter clockwise.

    So to calculate sines and cosines using trigonometry, and with x≡East and Y≡North, we subtract the bearing from 90°.

    For example, a bearing of 117° will be calculated as (90-117)=-27° in trigonometry.

    Now we're ready to sum the distances:

    The distances are:
    1. 4*60*50=12000m
    2. 2*60*50=6000m

    Bearing Angle
    231°T -> 90-231=-141°
    117°T -> 90-117=-27°

    leg Distance(D) Angle(A) Dcos(A) Dsin(A)
    1 12000 -141° -9325.75 -7551.84
    2 6000 -27° 5346.04 -2723.94
    Sum (x2,y2)=(-3979.71,-10275.78)
    Distance = sqrt(x2²+y2²)
    angle
    = arctan(-10275.78/-3979.71)
    Note that since both numbers are negative, angle is in 3rd quadrant
    = 248.83°(trig.)
    convert to bearing, subtract from 90 and add 360 if result is negative
    = (90-248.83)+360
    = 201.17°T

    Check all calculations please.

  2. Tammy

    Thank you so much for all your help you my friend are a legend! Sorry about the mistakes :0

Respond to this Question

First Name

Your Answer

Similar Questions

  1. Math

    A fishing boat leaves port at 11 miles per hour at a bearing of 210 degrees for 2 hours, then turns to a bearing of 250 degrees at 8 miles per hour for 4 hours, and finally changes to a bearing of 280 degrees at 7 miles per hour for …
  2. math

    A fishing boat leaves port at 11 miles per hour at a bearing of 210 degrees for 2 hours, then turns to a bearing of 250 degrees at 8 miles per hour for 4 hours, and finally changes to a bearing of 280 degrees at 7 miles per hour for …
  3. Math

    A fishing boat leaves port at 5 miles per hour at a bearing of 350∘ for 2 hours, then turns to a bearing of 40∘ at 12 miles per hour for 2 hours, and finally changes to a bearing of 180∘ at 10 miles per hour for 5 …
  4. Math

    A fishing boat leaves port at 5 miles per hour at a bearing of 350∘ for 2 hours, then turns to a bearing of 40∘ at 12 miles per hour for 2 hours, and finally changes to a bearing of 180∘ at 10 miles per hour for 5 …
  5. Math

    Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided …
  6. Math(DifferentQuestion,SameDescription)

    Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided …
  7. Math(PleaseHelp, NewEquation SameDescription)

    Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided …
  8. Vectors

    A fishing boat leaves port at 8 miles per hour at a bearing of 220∘ for 5 hours, then turns to a bearing of 270∘ at 11 miles per hour for 4 hours, and finally changes to a bearing of 300∘ at 9 miles per hour for 4 hours. At this …
  9. Math, Precalc

    A fishing boat leaves port at 4 miles per hour at a bearing of 80∘ for 3 hours, then turns to a bearing of 0∘ at 3 miles per hour for 4 hours, and finally changes to a bearing of 200∘ at 6 miles per hour for 5 hours. At this …
  10. math - trigonometry

    A bushwalking party leave P and walk on a bearing of 335(degrees) for 11.4km until they reach Q. From Q they walk on a bearing of 65(degrees) for 18.7km at which point they arrive at R. a) What is the distance between R and P to 3 …

More Similar Questions