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Solutions: Vectors and scalars

1. A student holds an A4 size piece of paper parallel to the ground at a height of 1.5m. An Ant walks in an anticlockwise (haha) direction around the edge of the paper starting in the top right hand corner at a speed of 20cms-1. As the ant is walking the paper is dropped and it falls to the ground, as it falls it moves forwards 50cm. If the time taken to fall to the ground is 1.5s, calculate the magnitude of the Ant's displacement.

Hint:

  • First find out how big a sheet of A4 paper is
  • The ant walks at 20cms-1, calculate how far it goes in 1.5s.
  • Knowing how far the ant walks find its place on the paper.
  • Use pythagorus in 3D to find the total displacement R2= x2 + y2 + z2

Solution:

2. An airplane takes off and flies due North at an angle of 45° to horizontal for 2km, then makes a sharp turn and flies horizontally due West for 4km. Calculate the magnitude of the resultant displacement (ignore the curvature of the Earth).

Hint:

  • To find the resultant displacement just add the vectors for the two parts of the motion together, the fact that it flies at an angle doesn't matter.

Solution:

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