Edexcel M1 — Question 7

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
TopicSUVAT in 2D & Gravity

7. Two stones are projected simultaneously from a point \(O\) on horizontal ground. Stone \(A\) is thrown vertically upwards with speed \(98 \mathrm {~ms} ^ { - 1 }\). Stone \(B\) is projected along the smooth ground in a straight line at \(24 \cdot 5 \mathrm {~ms} ^ { - 1 }\).
  1. Find the distances of the two stones from \(O\) after \(t\) seconds, where \(0 \leq t \leq 20\).
  2. Show that the distance \(d \mathrm {~m}\) between the two stones after \(t\) seconds is given by $$d ^ { 2 } = 24 \cdot 01 \left( t ^ { 4 } - 40 t ^ { 3 } + 425 t ^ { 2 } \right) .$$
  3. Hence find the range of values of \(t\) for which the distance between the stones is decreasing.