Hong Kong · Grade 12 · Practice Sheet 34

1. 1.

   In a triangle, a = 11, b = 16 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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2. 2.

   A force of 95 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Two masses 7,700 kg and 470 kg are 5 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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4. 4.

   Find the force needed to accelerate a 12 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the momentum of a 21 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A wave has frequency 87 Hz and wavelength 2.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Two masses 3,300 kg and 420 kg are 2 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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8. 8.

   A 35 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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9. 9.

   Find the momentum of a 29 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    An object with initial velocity 6 m/s accelerates at 3 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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11. 11.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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12. 12.

    Find the force needed to accelerate a 45 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    An object with initial velocity 2 m/s accelerates at 3.2 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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14. 14.

    In a triangle, a = 18, b = 7 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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15. 15.

    Two masses 4,500 kg and 570 kg are 20 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    Find the gravitational potential energy of a 14 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A device runs at 92 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Two masses 3,500 kg and 330 kg are 17 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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19. 19.

    A device runs at 114 V drawing 8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A force of 204 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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