Since they will collide the time taken for both to reach the intersection is the same.
Let the time taken by t.
Recall that for steady motion,
[tex]\begin{gathered} d=st \\ \text{ Where:} \\ d=\text{ the distance covered} \\ s=\text{ the speed} \\ t=\text{ the time} \end{gathered}[/tex]
Substitute d = 4 and s = 442 into the equation:
[tex]\begin{gathered} 4=442t \\ \text{ Dividing both sides by }442,\text{ it follows that:} \\ t=\frac{4}{442} \end{gathered}[/tex]
Therefore, the distance covered by the Coyote in this time is given by:
[tex]d=\frac{4}{442}\times481=\frac{74}{17}[/tex]
Using the Pythagorean Rule, it follows that the distance between Road Runner and the Coyote along the diagonal is given by:
[tex]h=\sqrt{(\frac{74}{17})^2+4^2}[/tex]
Since speed s for a body that travelled distance d in time t is given by:
[tex]s=\frac{d}{t}[/tex]
it follows that the required speed is given by:
[tex]-\sqrt{(\frac{74}{17})^2+4^2}\times\frac{442}{4}=-65\sqrt{101}[/tex]
Therefore, the required rate is -65√101 kph.
