1%Y. li. lin.A IY:10: 2 Problems of chapt.. →Problems of chapter 2 and 3:1. The polar coordinates of a point are r = 5.50 m and 0 = 240°. What are thecartesian coordinates of this point?2. The driver of a car drives 3.00 km north, 2.00 km northeast (45.0° east ofnorth). 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 answergraphically. 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 + 3C0, what are the components of C?4. The vectors A and B are given by A = 2i +3j andB = -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 expressionr = (3.00i - 6.00: 2 j) m. (a) Find expressions for the velocity andacceleration as functions of time. (b) Determine the particle's position andvelocity at = 1.00 s.6. A long-jumper leaves the ground at an angle of 20.0° above the horizontaland at a speed of 11.0 m/s. (a) How far does he jump in the horizontaldirection? (Assume his motion is equivalent to that of a particle.)7. An astronaut on a strange planet finds that she can jump a maximumhorizontal distance of 15.0 m if her initial speed is 3.00 m/s. What is thefree-fall acceleration on the planet?8. A tire 0.500 m in radius rotates at a constant rate of 200 rev/min. Find thespeed and acceleration of a small stone lodged in the tread of the tire (on itsouter edge). (Hint: In one revolution, the stone travels a distance cqual to thecircumference of its path, 2tr.)9. A student attaches a ball to the end of a string 0.600 m in length and thenswings the ball in a vertical circle. The speed of the ball is 4.30 m/s at itshighest point and 6.50 m's at its lowest point. Find the acceleration of theball when the string is vertical and the ball is at (a) its highest point and (b)its lowest point.

Answered: Image /qna-images/answer/c22f10ec-4ccf-42a5-86c7-afc2a33bf279.jpg

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.