91Ó°ÊÓ

A projectile is thrown from ground level with an initial velocity \(4 \mathrm{i}+3 \mathrm{j}\). It reaches its greatest height above ground level after: (a) \(0.24 \mathrm{~s}\) (b) \(0.3 \mathrm{~s}\) (c) \(0.18 \mathrm{~s}\) (d) \(3 \mathrm{~s}\) (e) \(5 \mathrm{~s}\).

A particle is projected with speed \(u\) at an elevation \(\alpha\) to the horizontal. Calculate the greatest height reached and the horizontal range. The maximum horizontal range a particle can achieve with an initial speed \(u\) is \(R .\) If a particle projected with speed \(u\) has a horizontal range \(\frac{3}{5} R\), calculate the two possible angles of projection. Show that the difference in the maximum heights attained with these angles of projection is \(\frac{2}{3} R\). (AEB)

A particle is projected with speed \(V\) at an angle \(\alpha\) to the horizontal. Show that its greatest height above the point of projection during its flight is \(\left(V^{2} \sin ^{2} \alpha\right) /(2 g)\). A ball is projected from a point at a heieht \(a\) above horizontal ground, with speed \(V\) at an angle \(\alpha\) to the horizontal. At the highest point of its flight it impinges normally on a vertical wall and rebounds. Show that the horizontal distance from the point of projection to the wall is \(\left(V^{2} \sin \alpha \cos \alpha\right) / g\) and that the time taken by the ball to reach the ground after the impact is \(\left.\sqrt{(} V^{2} \sin ^{2} \alpha+2 g a\right) / g\). \((\mathrm{U}\) of \(\mathrm{L})\)