a small airplane is dropping a probe in a remote area in antarctica in a narrowly specified location. the probe in a protective shell can not land any harder than with a maximum speed of 60m/sec at landing, while the plane has to move at a minimum speed of 30m/sec horizontally in order to stay airborne.

Question

if you are the pilot, you face the problem of having to decide from which height and distance from the location you can release the probe without destroying it . FIND A REASONABLE ANSWER FOR THIS PROBLEM

Answer 1

well, the vertical speed is 9.8t so the probe cannot fall for more than 60/9.8 = 6.12 seconds.

That means the plane cannot be higher than 183.67 m high.

so, at h meters altitude, with horizontal velocity v, the probe will land with speed

s = √(v^2+4h^2)
The probe will travel horizontally vt = v√(h/4.9) meters

So, we need
h <= 183.67
v >= 30
√(v^2+4h^2) <= 60

So, just pick a v and an h to fit those constraints.