Question
Physics for scientist and engineers (6th) Please explain how to rewrite vetors in terms of theirmagnitude and angle (counterclockwise from the +x direction). a) A displacement vector with an x component of +8.5 m and a ycomponent of -5.5m. b) a velocity vector with an x compnent of-75m/s and a y component of +35m/s c) a force vector with amagnitude of 50lb that is in the third quadrant with an x componentwhose magnitude is 40 lb. My gut feeling is to draw an x/y axis, and then use the A S TC, approach where All is positive in quadrant I, Sin is positive inquardrant II, Tan possitive in III and Cos possitive in quardrantIV. Am I on the right path? Can you please helpme Physics for scientist and engineers (6th) Please explain how to rewrite vetors in terms of theirmagnitude and angle (counterclockwise from the +x direction). a) A displacement vector with an x component of +8.5 m and a ycomponent of -5.5m. b) a velocity vector with an x compnent of-75m/s and a y component of +35m/s c) a force vector with amagnitude of 50lb that is in the third quadrant with an x componentwhose magnitude is 40 lb. My gut feeling is to draw an x/y axis, and then use the A S TC, approach where All is positive in quadrant I, Sin is positive inquardrant II, Tan possitive in III and Cos possitive in quardrantIV. Am I on the right path? Can you please helpme
Explanation / Answer
Displacement vector r = 8.5 i -5.5 j magnitude of r = [ 8.5^ 2 + -5.5 ^ 2 ] = 10.124 m let it makes an angle positive x axis then tan = -5.5 / 8.5 = -32.9 degrees In counterclockwise direction angle = 360- = 327.09degrees (b).velocity v = -75 i +35 j magnitude = [ -75 ^ 2 + 35 ^ 2 ] = 82.76 m /s let it makes an angle with negatice x-axis then tan = 35 / 75 = 25.01 degrees Angle with positve x-axis = 180 - = -154.9degrres