Question

Why is the component of A-y 61.40 but also 25? Help explain please

the first displacement, B the second, and C the third. We can estimate from the diagram that the vector sum R is about 10 m, 40° west of north. The angles of the vectors, measured counterclockwise from the +x axis, are 58, 216, and 270°. We have to find the components of each. Practice Problem 1.8 SOLVE The components of A are Consider four finalists in a treasure hunt who are brought to the center of a large, flat field. Each is given a meterstick, a compass, a calculator, a shovel, and (in a different order for each contestant) these three displacements Az Ay A cos θ A sin θ (72.4 m)(cos 58") (72.4 m)(sin 58") 38.37 m 61.40 m = = = = = = The table shows the components of all the displacements, the addition of components, and the other calculations. To find the magnitude R and direction θ, use the Pythagorean theorem R- /R, 2 + Ry2 and the definition of the inverse tangent. θ-tan-i Dy calculations systematically as in the table. Note that we have kept one too many significant figures in the components; we'll wait until the end to round to the correct number of significant figures 72.4 m, 32.0° east of north; RT Always arrange your component Figure 1 ▼ of 1 y (north) Distance A 72.4 m B 57.3 m C 17.8 m Angle 58° 216° 270° r component 38.37 m -46.36 m 0.00 m R,_-7.99 m y component 25.0 m 32.9 m -17.80 m Ry-9.92 m 36.0 57.3 m (-7.99 m)2+(9.92 m)2 12.7m tan-1 9.92 m-1290 39° west of north A 72.4 m 7.99 m 17.8 m The figure shows this resultant vector and its components 32.0 REFLECT The losers try to measure three angles and three distances totaling 147.5 m, 1 meter at a time. The winner measures only one angle and one much shorter distance x (east)

Answer 1

the first displacement, B the second, and C the third. We can estimate from the diagram that the vector sum R is about 10 m, 40° west of north. The angles of the vectors, measured counterclockwise from the +x axis, are 58, 216, and 270. We have to find the components of each. Practice Problem 1.8 SOLVE The components of A are Consider four finalists in a treasure hunt who are brought to the center of a large, flat field. Each is given a meterstick, a compass, a calculator, a shovel, and (in a different order for each contestant) these three displacements AzA cos (72.4 m)(cos 58°)38.37 m AyA sin (72.4 m) (sin 58°)61.40 m The table shows the components of all the displacements, the addition of components, and the other calculations. To find the magnitude R and direction 0, use the Pythagorean theorem R-R Ry2 and the definition of the inverse tangent, tan 1 Always ar calculations systematically as in the table. Note that we have kept one too many significant figures in the components; we'll wait until the end to round to the correct number of significant figures 72.4 m, 32.0° east of north; arrange your component Figure 1 Y of 1 y (north) Distance A 72.4 m В 57.3 m C 17.8 m Angle 58° 216° 270° r component 38.37 m -46.36 m 0.00 m R7.99 mRy -9.92 m y component 36.0 -33 6 g m -17.80 m 57.3 m (-7.99 m)2+(9.92 m)2 12.7m tan-19.92m 12939° west of north A 72.4 m 7.99 m 17.8 m C The figure shows this resultant vector and its components 32.0 REFLECT The losers try to measure three angles and three distances totaling 147.5 m, 1 meter at a time. The winner measures only one angle and one much shorter distance x (east) There was some misprinting rest is correct