A stone is thrown vertically upward with an initial speed from ground level

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A stone is thrown vertically upward with an initial speed

u

from ground level. Neglect air resistance. (i) Show that the total time of flight until the stone returns to the point of projection is

\dfrac{2u}{g}

. (ii) Prove that the maximum height

H

reached by the stone is

\dfrac{u^{2}}{2g}

. (iii) If the stone is required to stay in the air for exactly

6\,\text{s}

, calculate the initial speed that must be imparted and the corresponding maximum height attained.