Physics Assignment #2 Vector Direction and Magnitude Word Problems 1. What is the magnitude and heading of the vectors below: 2. Sketch the resultant vectors for the figures below: 3. What is the magnitude and heading for the resultant vectors in the following figures below? 4. Find the magnitude and heading for the resultant vectors from the figures below. 5. Given the following vector endpoint coordinates from (0, 0), sketch the vectors, and then determine the magnitude and direction of the resultant vector. ๐ โ =< 2, 3 >, ๐กโ =< 1,2 > ๐โ =< −2, 2 >, ๐โโ =< 0, −2 > 6. Given the resultant vector, determine the missing vector ๐โ, and it’s magnitude and heading ๐โ =< 0, −5 >, ๐โโ =< −3, 4 > 7. Given the following vectors below, find the resultant vector’s magnitude and heading. 8. Vector u has a magnitude of 53, and a direction of 0๏ฐ. Vector v has a direction of 295๏ฐ, and a magnitude of 10. Find the magnitude and direction of the resultant vector to the nearest whole number. 9. Vector u has a magnitude of 27 and a direction of 40°. Vector v has a magnitude of 34 and a direction of 58°. Find the magnitude and direction of the resultant to the nearest whole number. 10. A plane flies with a velocity of 52 m/s east through a 12 m/s cross wind blowing the plane south. Find the magnitude and direction (relative to due north) of the resultant velocity at which it travels. 11. A racing car is accelerating at 20 m/s2 70โฆ N of W. Find the acceleration of the car in the north direction and in the west direction. 12. An airplane is heading north with an airspeed of 325 miles/hr with a wind from the east at 55 miles/hr. What is the airplane’s velocity relative to the ground (ground speed)? Is the airplane’s ground speed faster or slower than the plane’s airspeed? Why? 13. A person walks 4 paces north, 6 paces northeast, 2 paces east and 5 paces west. What is their final location in vector form (<v>=ai+bj). 14. An airplane flies due west at 185 km/h with respect to the air. There is a wind blowing at 85 km/h to the northeast relative to the ground. What is the plane’s speed and direction with respect to the ground? 15. A plane is flying at a heading of 340° at 325 miles/hr. A tailwind is blowing 40° west of north at 40 miles/hr. Express the velocity of the plane as a result of these factors in vector form (<v>=ai+bj). 16. What is the ground speed and direction of the plane in #15? 17. A plane is flying with a heading of 170° at 460 miles/hr. A headwind is blowing in the direction 40° east of north at 40 miles/hour. What is the ground speed and direction of the airplane? 18. There is a wind blowing at 50 miles/hr from due South. A pilot wants his final ground speed to be 450 miles/hr, so that his ultimate course is at a heading of 300๏ฐ for his final destination. Find the direction and the speed of the plane that will be needed for the plane to meet these requirements given the wind. 19. Draw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of each component. |๐โ| = 10, 115° |๐โ| = 5, 210° 20. A plane is flying due East at 400km/hr into a Northwest headwind at 50km/hr. Find the direction the plane ends up flying and its groundspeed.
