Standard +0.3 This is a straightforward projectile motion problem requiring resolution of velocity components and application of constant acceleration equations. Students must find when the speed equals 18 m/s using v_x² + v_y² = 18², where v_x is constant and v_y = u_y - gt. The 'rising' condition simply means taking the earlier time solution. It's slightly above average difficulty due to requiring algebraic manipulation of the speed equation, but remains a standard M2 exercise with no novel insight required.
1 A particle is projected with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(50 ^ { \circ }\) above the horizontal. Calculate the time after projection when the particle has speed \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is rising.
1 A particle is projected with speed $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $50 ^ { \circ }$ above the horizontal. Calculate the time after projection when the particle has speed $18 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is rising.
\hfill \mbox{\textit{CAIE M2 2015 Q1 [4]}}