OCR MEI M1 2011 June — Question 6

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2011
SessionJune
TopicSUVAT in 2D & Gravity

6 In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors east and north respectively. Position vectors are with respect to an origin O . Time \(t\) is in seconds. A skater has a constant acceleration of \(- 2 \mathbf { j } \mathrm {~m} \mathrm {~s} ^ { - 2 }\). At \(t = 0\), his velocity is \(4 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and his position vector is \(3 \mathbf { j } \mathrm {~m}\).
  1. Find expressions in terms of \(t\) for the velocity and the position vector of the skater at time \(t\).
  2. Calculate as a bearing the direction of motion of the skater when \(t = 2.5\).