MHB Engineering Mechanics: depth of crater

[Joe_1234]

The depth of the crater of the Taal volcano was calculated in the following manner: From a helicopter flying vertically upward at 6m/s. A small bomb was released at the instant the helicopter was 20m above the crater surface. The sound of explosion was heard 9sec later. If the speed of sound is 335m/s, what is the depth of the crater?

 

[MarkFL]

I would begin by writing a function that expresses the helicopter's height (in meters) above the surface as a function of time (measured in seconds), where \(t=0\) corresponds to the instant the bomb was dropped.

Then, please answer these questions:

• If \(d\) is the depth of the crater, how far did the bomb fall and how long would it take to fall that distance (presumably ignoring drag)?
• How long would it take for the sound of the explosion to reach the rising helicopter?