1- A- Instructions for finding a buried treasure include the following: Go 448.6
ID: 3307831 • Letter: 1
Question
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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.
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- The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 50.5 north of west with a speed of 31.6 km/h. Exactly 3.20 hours later, the course of the hurricane shifts due north, and its speed slows to 24.5 km/h, as shown. How far from Grand Bahama is the hurricane 4.55 h after it passes over the island? Answer in units of km.
3-
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, 1 = 120 , 2 = 150 , 3 = 34 , and 4 = 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 .
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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
Explanation / Answer
1. r1 = 448.6 ( cos120 i + sin120 j)
r1 = -224.3i + 388.5 j
r2 = 254 ( cos156i + sin156j) = -232i + 103.3j
r3 = 491 ( cos232 i + sin232 j)
r3 = - 302.3 i - 386.9j
r = r1 + r2 + r3
= - 758.6 i + 104.9 j
(A) Magnitude = sqrt(758.6^2 + 104.9^2)
= 765.8 paces
(b) direction = 180 - tan^-1(104.9/758.6)
= 172 deg
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