Question

A weather balloon carrynig a data measurement(DM) is rising quickly at a constant velocity, U. when its 60m above ground, balloon pops and the dm experiences freefall. It reaches ground 4 seconds after the balloon pops. If DM set hits ground at speed greater than 40 ms-1 it will break.

Explain whether the DM set broke. showing your working clearly.

State whether the dm set would have broke if the weather balloon was moving at a constant velocity of -U if it pops

Answer 1

the height of the DM after the balloon pops is given by

y(t) = 60 + Ut - 4.9t^2
If y(4) = 0, then

60+4U-78.4 = 0
U = 4.6

The speed of the DM is given by
v(t) = U-9.8t
v(4) = U-39.2

So, as long as U > 0.8, the DM will hit the ground with v > -40m/s and will not break.