Question

A spy in a speed boat is being chased down a river by government officials in a faster craft. Just as the officials’ boat pulls up next to the spy’s boat, both boats reach the edge of a 4.6 m waterfall. The spy’s speed is 17 m/s and the officials’ speed is 28 m/s. How far apart will the two vessels be when they land below the waterfall? The acceleration of gravity is 9.81 m/s 2 . Answer in units of m.

Answer 1

Answer:

They are 7.4m apart.

Explanation:

Here we have a parabolic motion problem. we need the time taken to land so:

$Y=Yo+Vo*t+\frac{1}{2}*a*t^2$

considerating only the movement on Y axis:

$0=4.6-(9.81)*t^2\\t=0.68s$

Because we have a contant velocity motion on X axis:

$xs=vs*t\\xs=17m/s*(0.68s)\\xs=11.6m$

and

$xg=vg*t\\xg=28m/s*(0.68s)\\xg=19m$

the distance between them is given by:

$d=|xg-xs|\\d=7.4m$