Answer to Question #96696 in Physics for Joshua rivers

Question #96696
a vector has an x-component of -2.5 meters and a y-component of 4.2 meters. Express the vector in magnitude angle form.
1
Expert's answer
2019-10-17T11:13:19-0400

Let the vector a\bf a has components

ax=2.5ma_x=-2.5\:\rm m

ay=4.2ma_y=4.2\:\rm m

Thus, the magnitude of the vector a\bf a


a=ax2+ay2=(2.5)2+4.22=4.9ma=\sqrt{a_x^2+a_y^2}=\sqrt{(-2.5)^2+4.2^2}=4.9\:\rm m

The angle that vector a\bf a makes with positive x-direction


θ=tan1ayax=tan14.22.5=121\theta=\tan^{-1}\frac{a_y}{a_x}=\tan^{-1}\frac{4.2}{-2.5}=121^{\circ}

Answer: a=(4.9m;121){\bf a}=(4.9\:\rm m;121^{\circ})


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