Can anyone help confirm the answer I have to these 3 questions?

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1) 10.0 km
2) Magnitude: 253km/h Direction: N(9)E
3) Northwest and 2.6 minutes

1 Answer
Feb 2, 2017

Answer:

Please see below. I have somewhat different results, but you can follow the process and check.

Explanation:

(1) As hiker moves #6.0# km. east and then #8.0# km. north, his movement can be depicted in following figure.
enter image source here
Now as p Pythagoras theorem, his movement is #sqrt(6^2+8^2)=sqrt(36+64)=sqrt100=10# km.

(2) Again the movement of plane is shown in following diagram. The plane travels north at #250# #(km.)/(hr.)# for two hour and is then #500# #km.# north, but is displaced #40# #km.# to southwest.
enter image source here
The resultant displacement is given by solution of triangle for third side i.e. #sqrt(500^2+40^2-2xx40xx500xxcos135^@)#

= #sqrt(250000+1600+40000xx0.7071)#

= #sqrt279884=529.04#

and resultant velocity is #529.04/2=264.52# #(km)/(hr.)# towards east at an angle #theta# from north given by #sintheta/40=sin135^@/529.04#

i.e. #sintheta=(40xx0.7071)/529.04# and #theta=3.065^@#

(3) As Andy can paddle canoe at #1.2# #m/s#, he covers #200m# in #200/1.2# seconds. During this period river current sends him #200/1.2xx0,4=200/3m# east.
enter image source here
As such he should paddle towards west and as distance covered is

#sqrt(200^2+(200/3)^2)=200/3sqrt10=210.82#

and time taken is #210.82/1.2=175.7# second or #175.7/60=2.93# minutes.