In a second contest, the three displacements given are 70.6 m , 51 degrees west of north; 15.7 m straight north; and 90.7 m, 43 degrees south of east. What magnitude does the winner calculate for the displacement to find the keys to the Porsche?
I know that the resultant vector is found with the 3 displacements by adding their x/y components. I need to find magnitude of the resultant and the angle of the resultant (in degrees south east) Please show the steps.
Help with physics homework! The magnitude keeps turning out as 9.34 m.?
2018-02-14 12:09 pm
回答 (3)
2018-02-14 4:32 pm
x-component of the resultant displacement
= [70.6 cos(90° + 51°) + 15.7 cos(90°) + 90.7 cos(-43°)] m
= 11.5 m
y-component of the resultant displacement
= [70.6 sin(90° + 51°) + 15.7 sin(90°) + 90.7 sin(-43°)] m
= -1.73 m
Magnitude of displacement
= √[(11.5)² + (-1.73)²] m
= 11.6 m
= [70.6 cos(90° + 51°) + 15.7 cos(90°) + 90.7 cos(-43°)] m
= 11.5 m
y-component of the resultant displacement
= [70.6 sin(90° + 51°) + 15.7 sin(90°) + 90.7 sin(-43°)] m
= -1.73 m
Magnitude of displacement
= √[(11.5)² + (-1.73)²] m
= 11.6 m
2018-02-14 2:07 pm
displacement d1:
70.6 m ; 51° WoN
d1y = d1*cos 51 = 70.6*0.6293 = 44.430
d1x = -d1*sin 51 = -70.6*0.7771 = -54,867
displacement d2:
15.7 m ; N
d2y = 15.7
d2x = 0
displacement d3:
90.7 m ; 43° SoE
d3y = -d3*sin 43 = -90.7*0.6820 = -61.857
d3x = d3*cos 43 = 90.7*0.7314 = 66.334
Y = d1y+d2y+d3y = 44.430-61.857+15.700 = -1.727
X = d1x+d2x+d3x = -54.867+66.334 = 11.467
total displacement D :
D = √X^2+Y^2 = √1.727^2+11.467^2 = 11.60
heading = arctan(Y/X) = arctan -1.727/11.467 = -8.57 ° (8.57° SoE)
70.6 m ; 51° WoN
d1y = d1*cos 51 = 70.6*0.6293 = 44.430
d1x = -d1*sin 51 = -70.6*0.7771 = -54,867
displacement d2:
15.7 m ; N
d2y = 15.7
d2x = 0
displacement d3:
90.7 m ; 43° SoE
d3y = -d3*sin 43 = -90.7*0.6820 = -61.857
d3x = d3*cos 43 = 90.7*0.7314 = 66.334
Y = d1y+d2y+d3y = 44.430-61.857+15.700 = -1.727
X = d1x+d2x+d3x = -54.867+66.334 = 11.467
total displacement D :
D = √X^2+Y^2 = √1.727^2+11.467^2 = 11.60
heading = arctan(Y/X) = arctan -1.727/11.467 = -8.57 ° (8.57° SoE)
2018-02-14 12:58 pm
North component of 1st. displacement = (cos 51 x 70.6) = 44.43m.
Add to that the 15.7m. north component, = total north of 60.13 metres.
South component of 3rd. displacement = (sin 43 x 90.7) = 61.86 metres.
Net south movement = (61.86 - 60.13) = 1.73 metres.
West component of 1st. displacement = (sin 51 x 70.6) = 54.87 metres.
East component of 3rd. movement = (cos 43 x 90.7) = 66.3 metres.
Net east movement = (66.3 - 54.87) = 11.6 metres.
Resultant displacement from origin = sqrt.(1.73^2 + 11.6^2) = 11.73 metres.
Direction from origin = arctan (1.73/11.6) = 8.5 degree south of east, or from end point to origin is 8.5 degrees north of west.
I have not rechecked my work.
Add to that the 15.7m. north component, = total north of 60.13 metres.
South component of 3rd. displacement = (sin 43 x 90.7) = 61.86 metres.
Net south movement = (61.86 - 60.13) = 1.73 metres.
West component of 1st. displacement = (sin 51 x 70.6) = 54.87 metres.
East component of 3rd. movement = (cos 43 x 90.7) = 66.3 metres.
Net east movement = (66.3 - 54.87) = 11.6 metres.
Resultant displacement from origin = sqrt.(1.73^2 + 11.6^2) = 11.73 metres.
Direction from origin = arctan (1.73/11.6) = 8.5 degree south of east, or from end point to origin is 8.5 degrees north of west.
I have not rechecked my work.
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