1. (a) x, y, z, coordinates become coefficients for unit vectors i, j, and k. (b) Pythagorean theorem and inverse tan.
3. (a) Difference between final and initial position vecorts gives displacement vector.. (b) To be in a plane parallel with 2 axes, coefficient of the third unit vector must be 0.
5. (a) Pythagorean theorem and inverse tan. (b) avg. vel. = displacement / elapsed time (c) avg. speed = total distance / elapsed time
10. (a) Find change in velocity (final - initial): subtract coefficients of i, j, and k. Then avg a = change in velocity / elapsed time, so divide each term by 4.0 s. (b) Pythagorean theroem and inverse tan.
11. (a) Velocity is 1st derivative of position function. (b) Acceleration is 2nd derivative of position.
22. (a) Free fall problem (b) Use time from part a (c) free fall problem
27. (a) Find horizontal component of velocity, solve for time (b) Find vertical component of velocity, use free fall equation with initial velocity (c) Horizontal component remains constant; vertical component calculated with free fall equaiton and intial velocity from part (b). (d) If vy > 0, ball is going up, if < 0, going down.
62. (a) Speed = total distance / elapsed time =circumference / period; don't forget to add in earth's radius. (b) This acts as a centripetal acceleration.
67. (a) Use constant acceleration equation and solve for v. (b) Convert speed to m/min, then divide by circumference to get rev/min
73. (a) Choose a direction to be positive, then add velocities. (b) Use answer from (a) boat - ground velocity and add to child boat - ground velocity. Watch the signs.
80. Relative to the car, the snowflake has a vertical and horizontal component of motion. Set up a vector triangle and solve for the angle.
99. (a) Find the time of flight using distance and horizontal component of initial velocity. Then find vertical position using free fall equation and initial velocity as the vertical component. (b) Horizontal component is constant, found in part (a). Combine two vectors to get resultant unsing Pythagorean theorem.