Classical Mechanics (Kibble & Berkshire) · Problem 4.21

Linear oscillations — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · projectile-mortar-cliff

Problem

A mortar gun, with a maximum range of 40 m on level ground, is placed on the edge of a vertical cliff of height 20 m overlooking a horizontal plain. Show that the horizontal range

R

of the mortar gun is given by

R = 40\left\{\sin\alpha + \left(1 + \sin^2\alpha\right)^{\frac{1}{2}}\right\}\cos\alpha,

where

\alpha

is the angle of elevation of the mortar above the horizontal. [Take

g = 10\text{ m s}^{-2}

.] Evaluate

R

(to the nearest metre) when

\alpha = 45^\circ

and

35^\circ

and confirm that

\alpha = 45^\circ

does not yield the maximum range. [Do not try to find the optimum projection angle this way. See Problem 4.22 below.]

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