1. The polar coordinates of a point are r = 5.50 m and 0 = 240°. What are the cartesian coordinates of this point? 2. The driver of a car drives 3.00 km north, 2.00 km northeast (45.0° east of north). 4.00 km west, and then3.00 km southeast (45.0° east of south). Where does he end up relative to his starting point? Work out your answer graphically. Check by using components. 3. Vector A has x and y components of -8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and -6.60 cm, respectively. If A - B+ 3C=0, what are the components of C? 4. The vectors A and B arc given by A = 2i +3j and B = -i+2j. (a) Determine the scalar product A.B. (b) Find the angle 0 between A and B. (c) Determine the vector product AXB. 5. The vector position of a particle varies in time according to the expression r = (3.00i - 6.001 2 j) m. (a) Find expressions for the velocity and acceleration as functions of time. (b) Determine the particle's position and velocity at i= 1.00 s. 6. A long-jumper leaves the ground at an angle of 20.0° above the horizontal and at a speed of 11.0 m/s. (a) How far does he jump in the horizontal direction? (Assume his motion is equivalent to that of a particle.) 7. An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 15.0 m if her initial speed is 3.00 mis. What is the free-fall acceleration on the planet? 8. A tire 0.500 m in radius rotates at a constant rate of 200 rev/min. Find the speed and acceleration of a small stone lodged in the tread of the tire (on its outer edge). (Hint: In one revolution, the stone travels a distance cqual to the circumference of its path, 2ar.) 9. A student attaches a ball to the end of a string 0.600 m in length and then swings the ball in a vertical circle. The speed of the ball is 4.30 m/s at its highest point and 6.50 m/s at its lowest point. Find the acceleration of the ball when the string is vertical and the ball is at (a) its highest point and (b) its lowest point.

2. Vector has a magnitude of 36 m and direction of 240°. The vector has a magnitude of 18 m and direction of 120°. Find the magnitude and direction of the resultant vector. 3. A student standing at the edge of the roof of a building throws a ball with an initial speed of 20 m/s at an angle of 30° above the horizontal. The ball travels 52.0 m horizontally before landing on horizontal ground below. (a) How tall is the building? (b) What is the final velocity of the ball right before its impact on the ground.

The two vectors ⃗a and ⃗b in the figure above have equal magnitudes of 10.0 m. Find ... (a)  . . . the x component of their vector sum ⃗r (b)  . . . the y component of their vector sum ⃗r (c). . . the magnitude of   ⃗r (d) ] . . . the angle  ⃗r makes with the positive direction of the x axis.

You fly 35.0 km in a straight line in still air in the direction 31.0° south of west. a) Find the distances you would have to fly straight south and then straight west to arrive at the same point. 18.0263 30.0009 30.0792 km South b) Find the distances you would have to fly first directly south-west and then directly north-west. 7.49958 km West km South-West km North-West