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Problems: 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 Ants displacement.

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).

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