____ | \(x_a = x + y + a t\) |

\(x_b = x + b t – g t^2 / 2\) | |

\(x_c = c t – h t^2 / 2\) |

A and B just make contact (equal distance and speed at time \(t\)):

____ | \(x+y+at=x+b t-g t^2 / 2\) | |

\(a=b – g t\) | ||

==> \(t=(b-a)/g\), \(2 g y= (b-a)^2\) |

B and C just make contact (equal distance and speed at time \(t\)):

____ | \(x + b t – g t^2 /2 = c t – h t^2 / 2\) | |

\(b – g t = c – h t\) | ||

==> \(t=(c- b) / (h – g)\), \(2 x (h – g)=(c-b)^2\) |

The two events above happen at the same time:

____ | \((b-a)/g=(c-b)/ (h – g)\) | |

==> \((b – a)h=(c-a)g\) |

B and C come to a halt at times \(t_b\) and \(t_c\) respectively at a distance \(d\) apart:

____ | \(d=(x+b t_b-g (t_b)^2/2)-(c t_c – h (t_c)^2/2)\) | |

\(b – g t_b=c-h t_c = 0\) | ||

==> \(2(x – d) = c^2/h – b^2 / g\) |

Eliminating \(g\), \(h\) and \(y\) now gives:

____ | \(x=(b/a-1)(c/a-1)d\) |

Substituting \(a=30\), \(b=40\) and \(c=50\) with \(d=45\) yards gives \(x\) as \(10\) yards.

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