CHAPTER 3 HOMEWORK
1. (P.70. Ex.6) Vector V1 is 6.0units long and points along the negative x axis. Vector V2 is 4.5 units long and points at +45° to the positive x axis. (a) What are the x and y components of each vector? (b) Determine the sum V1 + V2 (magnitude and angle).
2. (p.70 Ex.14) For the vectors given in Fig. 3-41, determine (a) A - B + C, (b) A + B - C, and (c) C - A -B.
3. (p.71 Ex.21) A car is moving with speed 18.0m/s due south at one moment and 27.5m/s due east 8.00s later. Over this time interval. determine (a) its average velocity, (b) its average acceleration (magnitude and direction for both). and (c) its average speed. [Hint: Can you determine all these from the information given?]
4. (p.71. Ex.30) A ball is thrown horizontally from the roof of a building 9.0m tall and lands 8.5m from the base. What was the ball's initial speed?
5. (p.72 Ex.39) A projectile is fired with an initial speed of 51.2m/s at an angle of 44.5° above the horizontal on a long flat firing range. Determine (a) the maximum height reached by the projectile, (b) the total time in the air, (c) the total horizontal distance covered (that is, the range), and (d) the velocity of the projectile 1.50s after firing.
6. (p.73 Ex.54) What is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 45rpm (revolutions per minute) if its diameter is 30cm?
7. (p.74 Ex.62) An airplane is heading due south at a speed of 550 km/h. If a wind begins blowing from the southwest at a speed of 90.0 km/h (average), calculate: (a) the velocity (magnitude and direction) of the plane, relative to the ground, and (b) how far off course it will be after 12.0 min if the pilot takes no corrective action. [Hint: First draw a diagram.]
8.* (P.72 p.25) The position of a particle is given by r = (6.0cos3.0ti + 6.0sin3.0tj) meters. Determine (a) the velocity vector, v and (b) the acceleration vector a. (c) What is the path of this particle? [Hint: Determine r = |r|.] (d) What is sthe relation between r and a (give a formula), and between r and a (give an angle)? (e) Show that a = v2/r.
9.* (p.73 Ex.49) A person stands at the base of a hill that is a straight incline making an angle f with the horizontal. For a given initial speed v0, at what angle q (to the horizontal) should objects be thrown so that the distance d they land up the hill is as large as possible?