2005 Paper 2 Q10

Year: 2005
Paper: 2
Question Number: 10

Course: LFM Pure and Mechanics
Section: Projectiles

Difficulty: 1600.0 Banger: 1465.9

projectiles collision simultaneous equations trigonometric arcsin quadratic horizontal ground

Problem

The points \(A\) and \(B\) are \(180\) metres apart and lie on horizontal ground. A missile is launched from \(A\) at speed of \(100\,\)m\,s\(^{-1}\) and at an acute angle of elevation to the line \(AB\) of \(\arcsin \frac35\). A time \(T\) seconds later, an anti-missile missile is launched from \(B\), at speed of \(200\,\)m\,s\(^{-1}\) and at an acute angle of elevation to the line \(BA\) of \(\arcsin \frac45\). The motion of both missiles takes place in the vertical plane containing \(A\) and \(B\), and the missiles collide. Taking \(g =10\,\)m\,s\(^{-2}\) and ignoring air resistance, find \(T\). \noindent [Note that \(\arcsin \frac35\) is another notation for \(\sin^{-1} \frac35\,\).]

No solution available for this problem.

Rating Information

Difficulty Rating: 1600.0

Difficulty Comparisons: 0

Banger Rating: 1465.9

Banger Comparisons: 2

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Problem source

The points $A$ and $B$ are $180$ metres apart and lie 
 on  horizontal ground. 
A missile is launched  from $A$ 
at  speed of $100\,$m\,s$^{-1}$ and at an
acute angle of elevation to the 
line $AB$ of $\arcsin \frac35$. A time $T$ seconds later,
an anti-missile missile  is launched from $B$, 
at speed of $200\,$m\,s$^{-1}$ 
and at an acute 
angle of elevation to the line $BA$ of $\arcsin \frac45$.    
The motion of both missiles
takes place in the vertical plane containing $A$ and $B$, and the 
missiles collide.
Taking $g =10\,$m\,s$^{-2}$ and ignoring air resistance,
find $T$.
\noindent
[Note that $\arcsin \frac35$ is another notation for $\sin^{-1} \frac35\,$.]

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