Engineering Mechanics: depth of crater

Click For Summary
SUMMARY

The depth of the Taal volcano crater was calculated using a physics problem involving a helicopter ascending at 6 m/s and a bomb dropped from 20 m above the crater. The sound of the explosion was heard 9 seconds later, with the speed of sound at 335 m/s. The calculations reveal that the bomb falls a distance of \(d\) meters, taking approximately \(t\) seconds to reach the crater, while the sound takes additional time to travel back to the helicopter. This problem illustrates the application of kinematic equations and sound propagation in determining geological features.

PREREQUISITES
  • Basic understanding of kinematic equations
  • Knowledge of sound propagation and speed of sound
  • Familiarity with physics concepts related to free fall
  • Ability to perform calculations involving time, distance, and speed
NEXT STEPS
  • Study kinematic equations for uniformly accelerated motion
  • Learn about the principles of sound propagation in different mediums
  • Explore free fall dynamics and the effects of gravity
  • Investigate real-world applications of physics in geological studies
USEFUL FOR

Students in physics, engineers involved in geological assessments, and anyone interested in the practical applications of mechanics in understanding natural phenomena.

Joe_1234
Messages
24
Reaction score
0
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?
 
Mathematics news on Phys.org
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?
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 16 ·
Replies
16
Views
5K
  • · Replies 22 ·
Replies
22
Views
61K
Replies
3
Views
4K
  • · Replies 1 ·
Replies
1
Views
10K
  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 4 ·
Replies
4
Views
9K
  • · Replies 2 ·
Replies
2
Views
3K