1. Vecor 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 relative to the positive x-axis?
a. 80 degrees
b. 10 degrees
c. 90 degrees
d. 100 degrees
2. A hiker walks 4.5 km at an angle of 45 degrees north of west. Then the hiker walks 4.5 km south. What is the magnitude and direction of the hiker's total displacement?
a. 3.5 km, 22 degrees south of west
b. 3.5 km; 22 degrees north of west
c. 6.4 km, 45 degrees north of west
d. 6.4 km; 22 degrees south of west
3. A gorilla weighs 8.00 X 10^2 N and swings from vine to vine. As the gorilla grabs a new vine, both vines make an angle of 30 degrees with the vertical. In such a condition of static equilibrium, what is the net force on the vine?
a. 924 N
b. 433 N
c. 196 N
d. 461 N
4. An Olympic skier moving at 20.0 m/s down a 30 degree slope encounters a region of wet snow and slides 145 m before coming to a halt. What is the coefficient of friction between the skis and the snow?
a. 0.540
b. 0.740
c. 0.116
d. 0.470
5. Which of the following energy forms is associated with an object's interaction with the environment?
a. potential energy
b. kinetic energy
c. mechanical energy
d. nonmechanical energy
6. A 1.00 X 10^3 kg sports car accelerates from rest to 25.0 m/s in 7.50 s. What is the average power output of the automobile engine?
a. 20.8 kW
b. 30.3 kW
c. 41.7 kW
d. 52.4 kW
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#6 is C.
#2 is A
3. D
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1. To find the direction of the resultant vector, we need to determine the angle it makes with the positive x-axis.
- Vector A is 3 units in length and points along the positive x-axis.
- Vector B is 4 units in length and points in a direction 150 degrees from the positive x-axis.
To find the angle between the positive x-axis and Vector B, we subtract 150 degrees from 180 degrees (since Vector B is 150 degrees from the positive x-axis in the clockwise direction):
180 degrees - 150 degrees = 30 degrees
Therefore, Vector B makes an angle of 30 degrees with the positive x-axis.
Since the resultant is the vector sum of Vector A and Vector B, the direction of the resultant vector will be the angle it makes with the positive x-axis. We can find this angle by adding the angle of Vector A (which is 0 degrees since it points along the positive x-axis) with the angle of Vector B:
0 degrees + 30 degrees = 30 degrees
Therefore, the direction of the resultant vector relative to the positive x-axis is 30 degrees.
The answer is not provided in the options given.
2. To find the magnitude and direction of the hiker's total displacement:
- The hiker walks 4.5 km at an angle of 45 degrees north of west.
- Then, the hiker walks 4.5 km south.
To find the magnitude of the hiker's total displacement, we need to add the magnitudes of the individual displacements:
4.5 km (north of west) + 4.5 km (south) = 9 km
The magnitude of the hiker's total displacement is 9 km.
To find the direction of the hiker's total displacement, we need to find the angle it makes with the west direction. Since the hiker walks north of west and then south, the total displacement will be south of the initial west direction.
The angle between the total displacement and the west direction can be found by subtracting the angle at which the hiker walks north of west from 180 degrees:
180 degrees - 45 degrees = 135 degrees
Therefore, the direction of the hiker's total displacement is 135 degrees south of west.
The answer is not provided in the options given.