HSC Physics Projectiles

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A tutorial sheet of harder questions on projectiles is given below. Unless otherwise indicated, neglect air resistance and take g = 9.8 ms -2 .

  1. A ball is thrown at 65 m/s at 32° to the horizontal. At what height does it strike a vertical wall 53 m from the point of projection? [28.6m]
  2. A stone is projected at 24 m/s and strikes a wall 37 m from the point of projection at a height of 15 m above the level of projection. What are the angles of projection to the horizontal? [47.8°,64.3°]
  3. A stone is thrown at 47 m/s at 35° above the horizontal from the edge of a cliff. The stone strikes the sea at an angle of 14° below the horizontal. What is the height of the cliff? [32.4m]
  4. A projectile is thrown at 13° below the horizontal from the edge of a cliff. It hits the sea at 135 m/s at an angle of 23° below the horizontal. What is the speed of projection? [127.5m/s]
  5. A projectile is thrown from a cliff and strikes the sea 56 m from the foot of the cliff at 97 m/s at 49° below the horizontal. What is the speed of projection? [90.7m/s]
  6. If a projectile strikes the sea at 140 m/s at 35° below the horizontal after being in flight for 12.0 s, what is the angle at which it was projected? [+18.0°]
  7. A projectile strikes the sea 65.0 m from the base of a cliff of height 127 m after being projected at 92.0 m/s. What is the angle of projection to the horizontal? [-60.9°]
  8. When a projectile lands below its initial level the maximum horizontal range is obtained at an angle of projection less than 45°. In shotput the shot leaves the hand at a height h above the ground at a speed u. Show that the angle of projection above the horizontal for maximum range is given by tan𝜽=1/(√(1+2gh/v2)).
  9. A projectile is thrown at an angle of 45° to the horizontal. Sketch, on the same axes, the path of the projectile when (i) air resistance is neglected, (ii) air resistance is included.
  10. A horizontal tunnel has a height of 3.00 m. A ball is thrown inside the tunnel with an initial speed of 18.0 m/s. What is the greatest horizontal distance the ball can travel before it bounces for the first time?[25.5m]

IB Physics Electric and Magnetic Fields

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A tutorial sheet on electric and magnetic fields follows.

  1. A charge +Q is at rest in the laboratory. Show the electric field around the charge in the laboratory reference frame.
  2. A charge +Q moves to the right at a constant velocity v relative to the laboratory. Draw the electric field of the charge (i) in the reference frame of the charge, (ii) in the laboratory reference frame.
  3. Two charges, +Q and +Q, both move to the right at a constant velocity v relative to the laboratory on parallel paths. In the reference frame of the charges, the line joining the charges is perpendicular to the velocity of the charges and has length d. Determine the magnitude of the force between the charges in (i) the reference frame of the charges, (ii) the laboratory reference frame.
  4. A current I flows in the same direction in each of two long parallel wires. Determine the force between the wires in (i) the laboratory reference frame, (ii) a refernce frame moving parallel to the wires at the speed of the charges.
  5. An electric field exists in the laboratory reference frame S. A reference frame S' moves at a constant velocity relative to the laboratory frame. (i) is an electric field present in s' ? (ii) is a magnetic field present in S' ?
  6. A magnetic field exists in the laboratory reference frame S. A reference frame S' moves at a constant velocity relative to the laboratory frame. (i) is an electric field present in S' ? (ii) is a magnetic field present in S' ?