Each of the displacement vectors A and B shown below has a magnitude of 3 m. i.

Question

Each of the displacement vectors A and B shown below has a magnitude of 3 m. i. Find graphically: A + B A - B B - A A - 2B In addition to the problem as given in the text, write down the x and y components of vectors A and B, and find components o f the resultant vector in each part obtained by algebraic calculation. Check consistency of the values of these components with the resultant vectors obtained graphically. Ax = Ay = Bx = By = (A+B)x = (A + B)y = (A-B)x = (A-B)y = (B-A)x = (B-A)y = (A-2B)x = (A-2B)y = In a game of American football, a quarterback takes the ball from die hue of scrimmage and runs backwards for 10 yards, and then sideways to the left, parallel to die line of scrimmage for 15 yards. At this point, he throws a forward pass at the angle of 60 degrees with respect to the line of scrimmage to the right. Ball flies 50 yards in this direction, before it is caught. What is the total distance between were die bull was initially spotted and were it was caught ? Set up a coordinate system for a drawing, with the .t-axis along the line of scrimmage pointing to die right and with the y-axis pointing downfield. Represent each step in ball motion by a displacement vector in your graph. Write down x and y components of each vector. Add components up to obtain components of the total displacement. Calculate magnitude of the total displacement vector.

Explanation / Answer

in all the questions to find graphically if there are two vectors A and B then using the two vectors as two sides of a parallellogram,drawing the diagonal from the point of intersection of A and B gives the resultant. this gives A+B if you want A-B,then put B in the opposite direction and then draw the diagonal. if you want A+2B,then extend B to 2B and then draw the diagonal hence answers are Ax=3cos30=2.598 Ay=3sin30=1.5 Bx=0 By=3 a)(A+B)x=3cos30=2.598 (A+B)y=3+3sin30=4.5 b)(A-B)x=3cos30-0=2.598 (A-B)y=1.5-3=-1.5 c)(B-A)x=0-3cos30=-2.598 (B-A)y=3-1.5=1.5 d)(A-2B)x=2.598-2*0=2.598 (A-2B)y=1.5-2*3=-4.5

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