Question

1-

A- Instructions for finding a buried treasure include the following: Go 448.6 paces at 120◦ , turn to 156◦ and walk 254 paces, then travel 491 paces at 232◦ . Find the magnitude of the resultant displacement from the starting point. Answer in units of paces.THE ANSWER IS (765.85) I am looking for answer B

B-What is the direction of the resultant displacement? Use counterclockwise from due East as the positive angular direction, between the limits of −180◦ and +180◦ . Answer in units of ◦

2-

A-Consider four vectors F~ 1, F~ 2, F~ 3, and F~ 4 with magnitudes F1 = 42 N, F2 = 29 N, F3 = 25 N, and F4 = 52 N, θ1 = 120 ◦ , θ2 = −150 ◦ , θ3 = 34◦ , and θ4 = −59◦ , measured from the positive x axis with counterclockwise positive. What is the magnitude of the resultant vector F~ = F~ 1 + F~ 2 + F~ 3 + F~ 4? Answer in units of N. THE ANSWER IS (8.83) I am looking for answer B

B-What is the direction of this resultant vector F~ , within the limits of −180◦ and 180◦ as measured from the positive x axis with counterclockwise positive ? Answer in units of ◦ .

4-

A-A hummingbird flies 2.3 m along a straight path at a height of 4.3 m above the ground. Upon spotting a flower below, the hummingbird drops directly downward 2.4 m to hover in front of the flower. a) What is the magnitude of the hummingbird’s total displacement? Answer in units of m.THE ANSWER IS (3.32) I am looking for answer B

B-How many degrees below the horizontal is this total displacement? Answer in units of ◦

Answer 1

1) Solution- Let us consider

V1= vector corresponding to first movement
V2= Vector corresponding to second movement
V3= Vector corresponding to third movement
Since moving a distance R at an angle theta means a "vector displacement" of
R*[cos(theta) , sin(theta)] where R*cos(theta) = x component and R*sin(theta)=y component
V1= 448.6*[ cos(120◦) , sin(120◦) ] =[-224.3 ,388.49]
V2= 254*[cos(156◦), sin(156◦) ]=[-232.04, -103.31]
V3= 491*[ cos( 232◦ , sin( 232◦) ] = [-302.29, -386.91]
Vnet = V1 + V2 + V3= [-758.63,-101.73]= [X,Y]

so, overall... distance moved = Sqrt[ X^2+Y^2] = 779.86 paces
and angle of momvent : atan(Y/X) = -(180-3.82) = -176.18