Determining Magnitude and Direction of Resultants with trigonometry

Determining Magnitude and Direction of Resultants with trigonometry

Important Trig concepts and equations The sum of all angles in ANY triangle equal 180 o n The following for right triangles ONLY n Pythagorean theorem a 2+b 2= c 2 (c is the hypotenuse) n SOHCAHTOA n sin = opp / hyp; cos = adj / hyp tan = opp/adj n

Another example If you are driving at 15. 0 m/s W and the wind is pushing you at 2. 00 m/s S, what is the magnitude and direction of your resultant? n 15. 1 m/s 7. 59 o S of W n

Another n If you move 4. 0 m E and 6. 0 m N what is the magnitude and direction of your resultant displacement?

x and y components of vectors

Terminology x-y components-two perpendicular vectors. n x and y refer to the x and y axis. n e. g. 5 m N and 3 m E n Until now in this chapter, I have been giving you x-y components and telling you to find the resultant. n

Reversing the process n A soccer ball is kicked 32 m at 24 o W of N. How far did it travel N and W? cos θ = adj/hyp cos 24 = y / 32 y = 29 m 32 m 24 o sin θ = opp/hyp sin 24 = x / 32 x = 13 m

Again n A boat attempts to cross a river by going directly South, however river current pushes them to the West. The boat ends up traveling 24 m/s at 13 o W of S, how fast was the boat going, how fast was the river going? Boat sohcahtoa 24 m/s 13 o W of S cos = adj/hyp boat’s velocity (vb) cos 13 = vb/24 vb = 23. 38488 vb = 23 m/s S river’s velocity vr River sin = opp/hyp sin 13 = vr/24 vr = 5. 3988253 vr = 5. 4 m/s W

Neat thing about x and y components act completely independently of each other. n Meaning an objects direction in the y direction has absolutely no effect on it x direction motion. n

Homework If you walk 7. 0 m up stairs to the next floor at an angle of 35 o above the horizontal. How high is the second floor? How far forward have you walked? n If you walk 15 m E and 24 m S. What is the magnitude and direction of your resultant? n