I am not sure if I properly understanding how to solve a vector problem. Are the
ID: 1877256 • Letter: I
Question
I am not sure if I properly understanding how to solve a vector problem. Are the answers I have correct? If not, could somebody please explain the proper way to do these? Thank you in advance! (2) Finding vector components: (a) A person walks 200 m at 27 degrees north of east 200 10.454) 90.8m Ax 200cos92 (b) A car moves 60 m/s at 35 degrees west of south. Ay 60sin 35 OCO.S74)-34-4ms Ayane 60 (0,819)” q 9.1m/s (c) A rocket accelerates at 45 m/s2 at 65 degrees south of east. 5C0-423)--1.0 mist Ay5i (3) Finding the resultant vector: (a) A plane flies 120 km/hr at 30 degrees north of east with a wind speed of 34 A hr at 10 degrees south of eat. What is the resulting velosity of the pla3e 152-37m/r uithofei."What (b) An explorer walks 22.0 km north, then 47.0 km at 55- her resul Ay 22inge utan dislment? 8 41 F 69 A- 22 65116 sesuitant disptocement-24. 84 Km (e) Determine the resultant displacement when a smelly dog chases a bunny rabbit 25 m E, 34 m at 70 degrees east of north, and 30 m at 45 degrees west of north. AK-25 R. 53.16 13,3 45 5-2825-49 70" resuitant disptacements A 25 C42.42
Explanation / Answer
Q2.
let east be along +ve x axis, and north be along +ve y axis.
let i and j are unit vectors along x and y axis.
then when a person walks 200 m at 27 degrees north of east,
vector displacement=200*(cos(27) i+ sin(27) j)
hence x component=200*cos(27)=178.2 m
y component=200*sin(27)=90.798 m
part b:
car moves 60 m/s at 35 degrees west of south
in vector notation, velocity=60*(-sin(35) i -cos(35) j)
x component=-60*sin(35)=-34.414 m/s
y component=-60*cos(35)=-49.149 m/s
part c:
acceleration is given as 45 m/s^2 at 65 degrees south of east.
then vector=45*(cos(65) i -sin(65) j)
x component=45*cos(65)=19.0178 m/s^2
y component=-45*sin(65)=-40.7838 m/s^2
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