A fire-work shell is projected from ground level making an angle of with the…

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

Problem

A fire-work shell is projected from ground level making an angle of

60^{\circ}

with the horizontal and reaches a maximum height of

45\,\text{m}

before falling back to the ground. Work out the following in the order stated: (a) Derive an expression for the square of the initial speed

v_0^{\,2}

in terms of the given maximum height

H

and the angle of projection

\theta_0

. No numerical substitution is required in this part. (b) Using the result of part (a) and

g = 9.8\,\text{m s}^{-2}

, calculate the initial speed

v_0

(correct to one decimal place). (c) For the same projection, determine the total time of flight and the horizontal range. (Take

g = 9.8\,\text{m s}^{-2}