Classical Mechanics (Kibble & Berkshire) · Problem 4.25

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

Physics — Mechanics · projectile-inclined-plane

Problem

An artillery gun is located on a plane surface inclined at an angle

\beta

to the horizontal. The gun is aligned with the line of steepest slope of the plane. The gun fires a shell with speed

u

in the direction making an angle

\alpha

with the (upward) line of steepest slope. Find where the shell lands. Deduce the maximum ranges

R^U

R^D

, up and down the plane, and show that

\frac{R^U}{R^D} = \frac{1-\sin\beta}{1+\sin\beta}.