A hawk 79 m above ground sees a mouse directly below running due north at 3.0 m/s. If it reacts immediately, at what angle and speed must the hawk dive in a straight line, keeping a constant velocity, to intercept its prey in 11.0 s? Incidentally, the mouse escaped by jumping in a hole. What's the speed in m/s?

Question

anonymous · Answer

At 3m/s, the mouse would run a distance of 33 m. in 11 sec.
As the hawk is 79 m. directly above, this means that the straight-line distance the hawk will travel is sqrt (33^2 +79^2) m, approx. 85.615m.  Given that the hawk travels at a constant velocity over that entire distance, the average speed would be 85.615/11=7.8 m/s.  The angle of depression (azimuthal angle) would be invtan (79/33), approx. 67.3 degrees.
Hope that helped.