Select the correct answer. If v_(x)=0.40meters/second and v_(y)=3.00meters/second what is the value of Theta A. 82^circ B. 2^circ C. 4^circ D. 8^circ

To find the value of \(\Theta\), we need to determine the angle between the velocity components \(v_x\) and \(v_y\). The tangent of this angle is given by the ratio of the two velocity components:<br /><br />\[<br />\tan(\Theta) = \frac{v_y}{v_x}<br />\]<br /><br />Given:<br />\(v_x = 0.40 \, \text{m/s}\)<br />\(v_y = 3.00 \, \text{m/s}\)<br /><br />Substitute the values into the equation:<br /><br />\[<br />\tan(\Theta) = \frac{3.00}{0.40} = 7.5<br />\]<br /><br />To find \(\Theta\), take the arctangent (inverse tangent) of 7.5:<br /><br />\[<br />\Theta = \tan^{-1}(7.5)<br />\]<br /><br />Using a calculator to find the arctangent:<br /><br />\[<br />\Theta \approx 82^{\circ}<br />\]<br /><br />Therefore, the correct answer is:<br /><br />A. \(82^{\circ}\)