1996 Paper 1 Q11

Year: 1996
Paper: 1
Question Number: 11

Course: LFM Pure and Mechanics
Section: Projectiles

Difficulty: 1484.0 Banger: 1484.0

projectiles angle of projection speed of projection quadratic trigonometric parabolic trajectory algebraic manipulation

Problem

A particle is projected under the influence of gravity from a point \(O\) on a level plane in such a way that, when its horizontal distance from \(O\) is \(c\), its height is \(h\). It then lands on the plane at a distance \(c+d\) from \(O\). Show that the angle of projection \(\alpha\) satisfies \[ \tan\alpha=\frac{h(c+d)}{cd} \] and that the speed of projection \(v\) satisfies \[ v^{2}=\frac{g}{2}\left(\frac{cd}{h}+\frac{(c+d)^{2}h}{cd}\right)\,. \]

No solution available for this problem.

Rating Information

Difficulty Rating: 1484.0

Difficulty Comparisons: 1

Banger Rating: 1484.0

Banger Comparisons: 1

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Problem source

A particle is projected under the influence of gravity from a point
$O$ on a level plane in such a way that, when its horizontal distance
from $O$ is $c$, its height is $h$. It then lands on the plane
at a distance $c+d$ from $O$. Show that the angle of projection
$\alpha$ satisfies 
\[
\tan\alpha=\frac{h(c+d)}{cd}
\]
and that the speed of projection $v$ satisfies 
\[
v^{2}=\frac{g}{2}\left(\frac{cd}{h}+\frac{(c+d)^{2}h}{cd}\right)\,.
\]

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