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A map has been drawn using a scale of 1:10 000. What does 1 cm on the map represent in reality? Which of the following is a vector quantity: volume, time, weight, velocity?

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5 parts
1

100 m\text{100 m}

2

velocity\text{velocity}

3

scalar\text{scalar}

4

the same\text{the same}

5

a + b

Step-by-step solution

5 steps

Here are the solutions to the questions from the image:

Part 1· 3 steps

A map has been drawn of the local area using a scale of 1: 10 000. What does a distance of 1 cm on the map represent a real distance of?

  1. Understand the map scale.

    A scale of 1:10 000 means that 1 unit on the map corresponds to 10 000 units in real life.

  2. Calculate the real distance in centimeters.

    If 1 cm on the map, then the real distance is 1 cm×10000=10000 cm1 \text{ cm} \times 10 000 = 10 000 \text{ cm}.

  3. Convert the real distance to a more practical unit (meters).

    Since 1 m=100 cm1 \text{ m} = 100 \text{ cm}:

    10000 cm=10000100 m=100 m10 000 \text{ cm} = \frac{10 000}{100} \text{ m} = 100 \text{ m}

    A distance of 1 cm on the map represents a real distance of 100 m\boxed{\text{100 m}}.

Part 2

velocity\text{velocity}

Which of the following is a vector quantity? volume, time, weight, velocity.

A vector quantity is a physical quantity that has both magnitude and direction.

  • Volume has magnitude but no direction (scalar).
  • Time has magnitude but no direction (scalar).
  • Weight is a force, which has both magnitude and direction (vector).
  • Velocity has both magnitude (speed) and direction (vector).

Among the given options, both weight and velocity are vector quantities. However, in typical multiple-choice scenarios asking for "a" vector quantity, velocity is a very common and direct example.
The vector quantity is velocity\boxed{\text{velocity}}.

Part 3

scalar\text{scalar}

Quantities that may be specified simply by giving their magnitude are called ____ quantities.

Quantities that are defined only by their magnitude are known as scalar quantities.
The quantities are called scalar\boxed{\text{scalar}}.

Part 4

the same\text{the same}

Two vectors a and b are equal if and only if they have ____ magnitude and direction.

For two vectors to be considered equal, they must have the same magnitude and the same direction.
Two vectors a and b are equal if and only if they have the same\boxed{\text{the same}} magnitude and direction.

Part 5a + b

Find vector x in terms of a and b.

  1. Apply the triangle law of vector addition.

    The triangle law states that if two vectors are represented by two sides of a triangle taken in order, their resultant is represented by the third side taken in the opposite order.

  2. Write the vector equation based on the diagram.

    In the given triangle, vector 'a' and vector 'b' are arranged head-to-tail. Vector 'x' is the resultant vector, starting from the tail of 'a' and ending at the head of 'b'.
    Therefore, vector x is the sum of vector a and vector b.

    x⃗=a⃗+b⃗\vec{x} = \vec{a} + \vec{b}

    Vector x in terms of a and b is a+b\boxed{a + b}.

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