Question

1. In the figure below there are two vectors A and B. Draw/sketch (on the grids somewhere outside the gray box) a vector R that is the sum of the two, (i.e. R-A+B) Clearly label the resultant vector as R Use the grid from problem 1 to determine the horizontal and vertical components of the resultant vector (R, and Ry respectively). Consider each box to be 1.00m by 1.00m. 2. Ry- 3. For the vector given in problems 1. and 2. find the magnitude and direction (angle) of the resultant vector. 4. A ball is thrown initially at 40.0m/s in a direction of 30° above the horizontal. What are the initial horizontal and vertical components of velocity? Use appropriate symbols and units

Answer 1

Vertical-bar A^vector Vertical-bar = 2 cm Vertical-bar B^vector Vertical-bar = squareroot 9 + 4 = 3.61 cm alpha = cos^-1 (2/3) = 48.2 degree therefore Vertical-bar R Vertical-bar = squareroot A^2 + B^2 + 2AB cos alpha = squareroot (2)^2 + (3.61)^2 + 2 times 2 times 3.61 times cos (48.2) = 5.16 cm (Magnitude). Tan theta = B sin alpha/A + B cos alpha tan theta = 0.611 theta = 31.4 degree (Direction) therefore R_x = R sin theta = 5.16 times sin (31.4 degree) = 2.69 2.7 cm R_y = R cos theta = 5.16 times cos (31.4 degree) = 4.4 cm v = 40 m/s theta = 30 degree therefore v_x = V cos theta = 40 times cos 30 degree = 34.64 m/s V_y = V sin theta = 40 times sin 30 degree = 20 m/s.