Text questions that are similar to the ones below:
CQ 3.2, 3.4, 3.22
P 3.2, 3.21, 3.28, 3.29, 3.35, 3.36, 3.37, 3.40, 3.48, 3.53
Conceptual Questions:
1. For many 2- and 3-dimensional problems, a cartesian coordinate system is useful. a) what is a cartesian coordinate system? b) why is it useful? c) how would you choose to orient the coordinates for a particular analysis? (CQ-3.4)
2. List several vector quantities and say why they are vectors, not scalars. (CQ-3.2)
3. Suppose you are sitting on a train moving at constant speed v. What direction in the train car do you throw a ball so when it comes down you catch it? (CQ-3.22)
Numerical Problems:
4. A taxicab moves five blocks due north, five blocks due east and another two blocks due north. Assume all blocks are squares of equal size. What is the magnitude of the taxi's displacement from start to finish? (P-3.2)
5. Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 150 degrees from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added? (P-3.21)
6. Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 150 degrees from the positive x-axis. What is the direction of the resultant with respect to the positive x-axis? (P-3.28)
7. John throws a baseball from the outfield from shoulder height, at an initial velocity of 29.4 m/s with an initial angle of 30 degrees with respect to the horizontal. The ball is in its trajectory for a total interval of 3 s before the third baseman catches it at shoulder-height level (Assume air resistance is negligible). What is the ball's horizontal displacement? (P-3.29)
8. A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30 degrees with respect to the horizontal. What is the maximum vertical displacement that the ball reaches during its trajectory? (P-3.35)
9. A helicopter is traveling at 40 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground (g = 9.8 m/s2 and air resistance negligible)? (P-3.37)
ans: 60 m/s.
10. A rifle is aimed horizontally toward the center of a target 100 m away. If the bullet strikes 10 cm below the center, what was the velocity of the bullet (ignore air friction)? (P-3.36)
11. A jet airliner moving at 500 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30 degrees north of east. What is the new speed and direction of the aircraft? (P-3.53)
ans: 607 mph, 5.67 deg N of E.
12. A boat moves at 10 m/s relative to the water. If the boat is in a river where the current is 2 m/s, how long does it take the boat to make a complete round trip of 1000 m upstream followed by 1000 m back downstream relative to the land? (P-3.48)
13. A baseball leaves the bat with a speed of 44 m/s and an angle of 30 degrees above the horizontal. A 5 m high fence is located at a horizontal distance of 132 m from the point where the ball is struck. Assuming the ball leaves the bat 1 m above ground level, by how much does the ball clear the fence? (P-3.40)