Answer to Question #94552 in Mechanics | Relativity for stefanie

Question #94552
Two points in the xy plane have Cartesian coordinates (5.50, −4.00) m and (−6.00, 6.00) m.
(a) Determine the distance between these points.
m

(b) Determine their polar coordinates.
(5.50, −4.00) r = m
(5.50, −4.00) θ = ° counterclockwise from the +x-axis
(−6.00, 6.00) r = m
(−6.00, 6.00) θ = ° counterclockwise from the +x-axis
1
Expert's answer
2019-09-16T09:51:55-0400
A(5.50,4.00),B(6.00,6.00)A(5.50, -4.00),\quad B(-6.00, 6.00)

(a) The distance between points


d=(xAxB)2+(yAyB)2d=\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}

=(5.50+6.00)2+(4.006.00)2=15.2m=\sqrt{(5.50+6.00)^2+(-4.00-6.00)^2}=15.2\:\rm m

(b) The polar coordinates


r=x2+y2,θ=tan1yxr=\sqrt{x^2+y^2}, \quad \theta=\tan^{-1}\frac{y}{x}rA=(5.50)2+(4.00)2=6.80,r_A=\sqrt{(5.50)^2+(-4.00)^2}=6.80,

θA=tan1(4.005.50)=324,\theta_A=\tan^{-1}\left(\frac{-4.00}{5.50}\right)=324^{\circ},rB=(6.00)2+(6.00)2=8.49,r_B=\sqrt{(-6.00)^2+(6.00)^2}=8.49,

θB=tan1(6.006.00)=135\theta_B=\tan^{-1}\left(\frac{6.00}{-6.00}\right)=135^{\circ}

So


A(6.80,324),B(8.49,135)A(6.80, 324^{\circ}),\quad B(8.49, 135^{\circ})


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