Standard +0.8 This projectile question requires finding two specific points where the velocity vector makes 45° with horizontal, then calculating the horizontal distance between them. It demands understanding of velocity components, inverse trigonometry to find the times, and careful algebraic manipulation—going beyond routine projectile questions that typically ask for range or maximum height.
3 A stone is thrown with speed \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) above the horizontal from a point on horizontal ground. Find the distance between the two points at which the path of the stone makes an angle of \(45 ^ { \circ }\) with the horizontal.
3 A stone is thrown with speed $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $60 ^ { \circ }$ above the horizontal from a point on horizontal ground. Find the distance between the two points at which the path of the stone makes an angle of $45 ^ { \circ }$ with the horizontal.
\hfill \mbox{\textit{CAIE M2 2016 Q3 [5]}}