IB Physics Challenging Mechanics Questions

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A tutorial sheet of difficult mechanics questions is given below.

  1. A ball rolls horizontally from a table of height 2.0 m. On collision with the smooth horizontal floor the kinetic energy of the ball is reduced by one-half. At what speed does the ball leave the table if it strikes a vertical wall 1.0 m from the table at a height of 1/3 m above the floor? (0.75 m/s, 1.20 m/s, 1.92 m/s)
  2. Adapted from the Moscow Physics Problems (MPP) 1986-2005, 1.15. A projectile moves horizontally at 10.0 ms-1 at a height above the ground of 30.0 m. When it is 25.0 m from a vertical wall it explodes and disintegrates into many fragments flying in all directions and all having an initial speed of 20.0 ms-1 relative to the projectile. Find the area on the surface of the wall that will be hit by the debris. Assume that fragments hitting the ground do not bounce and ignore air resistance. ( 4673.91 m2 , x axis along initial direction of motion, max height on wall z = 50.19 m, hits wall at ground level at y = 61.75 m, g = 9.81 m s-2 )
  3. In the previous question the wall is not present. Determine the area on the ground that can be struck by debris from the explosion. (1.8007 ha, on x axis debris lands 104.14 m ahead and 28.73 m behind explosion point)
  4. In question 3 determine the time interval during which debris is hitting the ground. ( 4.08 s )
  5. In question 3 the explosion occurs at a vertical height of 30.0 m over an inclined plane of angle of elevation 20°. Determine the area on the incline on which debris lands. ( 1.1801 ha, debris lands a maximum 70.92 m ahead and 46.38 m behind, on the incline measured from the perpendicular to the plane through the explosion point )