1995 Paper 3 Q10

Year: 1995
Paper: 3
Question Number: 10

Course: LFM Pure and Mechanics
Section: Projectiles

Difficulty: 1700.0 Banger: 1500.0

projectiles projectile on slope inclined plane optimisation range maximisation trigonometric identity kinematics

Problem

A cannon is situated at the bottom of a plane inclined at angle \(\beta\) to the horizontal. A (small) cannon ball is fired from the cannon at an initial speed \(u.\) Ignoring air resistance, find the angle of firing which will maximise the distance up the plane travelled by the cannon ball and show that in this case the ball will land at a distance \[ \frac{u^{2}}{g(1+\sin\beta)} \] from the cannon.

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

Difficulty Comparisons: 0

Banger Rating: 1500.0

Banger Comparisons: 0

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Problem source

A cannon is situated at the bottom of a plane inclined at angle $\beta$
to the horizontal. A (small) cannon ball is fired from the cannon
at an initial speed $u.$ Ignoring air resistance, find the angle
of firing which will maximise the distance up the plane travelled
by the cannon ball and show that in this case the ball will land at
a distance 
\[
\frac{u^{2}}{g(1+\sin\beta)}
\]
from the cannon.

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