1.### Multiplying or dividing vectors by scalars results in

Answer:
Vectors

Explanation:

When multiplying or dividing vectors by scalars, the result is always a vector. This is because multiplying a vector by a scalar scales the magnitude of the vector without changing its direction, resulting in a new vector. Similarly, dividing a vector by a scalar also scales the magnitude of the vector, but in the opposite direction, still resulting in a vector. Therefore, the correct answer is vectors.

2.### For the winter, a duck flies 10.0 m/s due south against a gust of wind with a speed of 2.5 m/s. What is the resultant velocity of the duck?

Answer:
7.5 m/s south

Explanation:

The duck is flying south at a speed of 10.0 m/s, while the gust of wind is blowing north at a speed of 2.5 m/s. Since the gust of wind is against the duck's motion, it acts as a negative force. To find the resultant velocity, we subtract the wind speed from the duck's speed. Therefore, the resultant velocity of the duck is 7.5 m/s south.

3.### In a coordinate system, a vector is oriented at an angle with respect to the x-axis. The y-component of the vector equals the vector's magnitude multiplied by which trigonometric function?

Answer:
Sin θ

Explanation:

In a coordinate system, when a vector forms an angle θ with the x-axis, its y-component equals the vector's magnitude multiplied by the sine of that angle (Sin θ). This relationship arises from trigonometry and is fundamental in determining the vertical component of a vector's magnitude in relation to its angle with the x-axis.

4.### In a coordinate system, a vector is oriented at an angle with respect to the x-axis. The x-component of the vector equals the vector's magnitude multiplied by which trigonometric function?

Answer:
Cos θ

Explanation:

The x-component of a vector in a coordinate system is found by multiplying the magnitude of the vector by the cosine of the angle it makes with the x-axis. This is because the cosine function relates the adjacent side of a right triangle (which represents the x-component) to the hypotenuse (which represents the magnitude of the vector). Therefore, the correct answer is cos θ.

5.### What is the path of a projectile (in the absence of air resistance)?

Answer:
A parabola

Explanation:

In the absence of friction, the path of a projectile follows a parabolic trajectory. This is because the only force acting on the projectile is gravity, which causes it to accelerate downward. As a result, the projectile follows a curved path that is symmetric around its highest point. This trajectory is known as a parabola.

6.### A piece of chalk is dropped by a teacher walking at a speed of 1.5 m/s. From the teacher's perspective, the chalk appears to fall

Answer:
Straight down

Explanation:

From the teacher's perspective, the chalk appears to fall straight down because the teacher is walking at a constant speed and in a straight line. Since there are no external forces acting on the chalk horizontally, it will continue to move forward with the same speed as the teacher. However, gravity will cause it to accelerate vertically downwards, resulting in a straight downward fall from the teacher's point of view.

7.### A passenger on a bus moving east sees a man standing on a curb. From the passenger's perspective, the man appears to

Answer:
Move west at a speed that is equal to the bus's speed.

Explanation:

The passenger on the bus sees the man on the curb appear to move west at a speed that is equal to the bus's speed. This is because the bus is moving east, so the relative motion between the bus and the man is that the man appears to be moving in the opposite direction at the same speed as the bus.

8.### A car travels 100 kilometers to the north. What type of quantity is this travel distance?

Answer:
Vector

Explanation:

This travel distance is a vector quantity because it specifies both the magnitude (100 kilometers) and the direction (north). Vectors require both components to fully describe them. For instance, knowing a car traveled 100 kilometers is not enough to determine its final position; we also need to know the direction. In contrast, scalar quantities, like temperature or mass, do not involve direction, only magnitude. Therefore, because the travel distance provides directional information along with magnitude, it is classified as a vector quantity.

9.### If a force of 10 Newtons is applied to push a box to the right, what kind of physical quantity is this force?

Answer:
Vector

Explanation:

Force is a vector quantity because it has both magnitude (10 Newtons) and direction (to the right). This is fundamental in physics as forces not only act with a certain strength but also in a specific direction. The effect of a force depends on both how much force is applied and where it is directed. For example, pushing a box to the right with 10 Newtons will move it differently compared to pushing with the same force to the left. Thus, the directional component is essential, making force a vector.

10.### An object's mass is measured as 5 kilograms. What type of quantity is mass?

Answer:
Scalar

Explanation:

Mass is a scalar quantity because it only has magnitude and no direction. Scalars are fully described by a single value, without needing any directional information. Mass indicates how much matter is in an object and is not dependent on the direction. Whether an object is stationary or in motion, its mass remains the same and does not change with direction. For example, a mass of 5 kilograms is simply a measure of how much material the object contains, regardless of where it is or how it is moving. Thus, mass is categorized as a scalar quantity.

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