What would the total displacement be for the hummingbird in this problem?

A hummingbird flies 1.2 meters along a straight path at a height of 3.4 meters above the ground. Upon spotting a flower below, the hummingbird drops directly downward 1.4 meters to hover in front of the flower.





Can anyone PLEASE show me how to solve this problem?? THANK YOU.

What would the total displacement be for the hummingbird in this problem?
the 1.2 is extraneous info...





the bird is 3.4 m above ground, then is drops directly downward 1.4m. The total displacement is 3.4-1.4 = 2m





So the hummingbird has a displacement of 2m...
Reply:This is fairly simple!





Use SOH CAH TOA





Given:


angle = 90 degrees(obviously)


dx = 1.2 m


dy = 1.4 m





Find:


resultant displacement = ?





Solution:


(I use dR as resultant displacement)





dR^2 = dx^2 + dy^2


dR^2 = (1.2 m) ^2 + (1.4m)^2


dR^2 = 1.44 m^2 + 1.96 m^2


dR^2 = 3.4 m^2


dR = sqrt. 3.4 m^2


dR = 1.843908891 m


dR = 1.8 m





Thus, the displacement is 1.8 m South of East!





Good luck and God bless!
Reply:d


___c


|\ |


| \ |


| \|b


|______


a e





Consider the above diagram,Let line ae represent the ground,let the humming bird be at point d.thus ad=3.4m





The bird flies from d to c.Thus dc=1.2m





From c it spots a flower and goes down 1.4m to reach it.therefore cb=1.4m





Now displacement is the shortest distance.In this case the bird was initially at 'd'.from 'd' it flew to 'c' ant then to 'b'. the shortest distance to reach b is directly from d to b skipping c.





Now note,that a right angled triangle dcb is formed,with db as the hypotinuse and aslo the diplacement.





applying the pythogoras theorem


db= underroot of dc square + underroot of cb square


= 2 2


√dc + bc





= 1.5m(approx)