A 4kg rock is rolling 10m/s whats its kinetic energy 2. a 8kg cat is running 4m/s what the kenetic energy3. rolling a ball has 18 joules of kinetic energy and is rolling 3m/s whats the mass 4. a 4kg bird has 8 joules of kinetic energy how fast is it flying?

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Answers

4 parts
1

200 J200\ \text{J}

2

64 J64\ \text{J}

3

4 kg4\ \text{kg}

4

2 m/s2\ \text{m/s}

Step-by-step solution

12 steps

Part 1· 3 steps

a 4kg rock is rolling 10m/s whats its kinetic energy

  1. Identify the given values.

    Mass (mm) = 4 kg
    Velocity (vv) = 10 m/s

  2. Use the kinetic energy formula.

    The formula for kinetic energy is KE=12mv2KE = \frac{1}{2}mv^2.

  3. Substitute the values and calculate.

    KE=12×4 kg×(10 m/s)2KE = \frac{1}{2} \times 4\ \text{kg} \times (10\ \text{m/s})^2 KE=12×4 kg×100 m2/s2KE = \frac{1}{2} \times 4\ \text{kg} \times 100\ \text{m}^2/\text{s}^2 KE=2 kg×100 m2/s2KE = 2\ \text{kg} \times 100\ \text{m}^2/\text{s}^2 KE=200 JKE = 200\ \text{J}

    The kinetic energy of the rock is 200\ J.

Part 2

64 J64\ \text{J}

a 8kg cat is running 4m/s what the kenetic energy

  1. Identify the given values.

    Mass (mm) = 8 kg
    Velocity (vv) = 4 m/s

  2. Use the kinetic energy formula.

    The formula for kinetic energy is KE=12mv2KE = \frac{1}{2}mv^2.

  3. Substitute the values and calculate.

    KE=12×8 kg×(4 m/s)2KE = \frac{1}{2} \times 8\ \text{kg} \times (4\ \text{m/s})^2 KE=12×8 kg×16 m2/s2KE = \frac{1}{2} \times 8\ \text{kg} \times 16\ \text{m}^2/\text{s}^2 KE=4 kg×16 m2/s2KE = 4\ \text{kg} \times 16\ \text{m}^2/\text{s}^2 KE=64 JKE = 64\ \text{J}

    The kinetic energy of the cat is 64\ J.

Part 3

4 kg4\ \text{kg}

rolling a ball has 18 joules of kinetic energy and is rolling 3m/s whats the mass

  1. Identify the given values.

    Kinetic Energy (KEKE) = 18 J
    Velocity (vv) = 3 m/s

  2. Use the kinetic energy formula and rearrange for mass.

    The formula for kinetic energy is KE=12mv2KE = \frac{1}{2}mv^2.
    To find mass (mm), rearrange the formula:

    m=2KEv2m = \frac{2KE}{v^2}

  3. Substitute the values and calculate.

    m=2×18 J(3 m/s)2m = \frac{2 \times 18\ \text{J}}{(3\ \text{m/s})^2} m=36 J9 m2/s2m = \frac{36\ \text{J}}{9\ \text{m}^2/\text{s}^2} m=4 kgm = 4\ \text{kg}

    The mass of the ball is 4\ kg.

Part 4

2 m/s2\ \text{m/s}

a 4kg bird has 8 joules of kinetic energy how fast is it flying?

  1. Identify the given values.

    Mass (mm) = 4 kg
    Kinetic Energy (KEKE) = 8 J

  2. Use the kinetic energy formula and rearrange for velocity.

    The formula for kinetic energy is KE=12mv2KE = \frac{1}{2}mv^2.
    To find velocity (vv), rearrange the formula:

    v2=2KEmv^2 = \frac{2KE}{m} v=2KEmv = \sqrt{\frac{2KE}{m}}

  3. Substitute the values and calculate.

    v=2×8 J4 kgv = \sqrt{\frac{2 \times 8\ \text{J}}{4\ \text{kg}}} v=16 J4 kgv = \sqrt{\frac{16\ \text{J}}{4\ \text{kg}}} v=4 m2/s2v = \sqrt{4\ \text{m}^2/\text{s}^2} v=2 m/sv = 2\ \text{m/s}

    The bird is flying at 2\ m/s.

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