Math-102-Session-5-Applications-Level-Bombing-1.pptx

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1. TRIGONOMETRY Math 102 Instructor: Angelo C. Gutierrez Jr. Session 5. Applications: Level Bombing

2. applications 2 Level Bombing

3. 3 In the given figure, Let P represent an airplane flying horizontally at the time when a bomb is released to hit a target T . At the moment of release, the bomb has the same speed as P . Let A be directly under P at the same level as T .

4. 4 Then, as a crude approximation, let us assume that the resistance of the air will have a negligible effect on the path of the bomb, or in other words, that the bomb will act as if it were falling in a vacuum.

5. 5 Then, the bomb falls in the vertical plane PAT with a speed forward equal to that of the airplane, which will therefore be at P 1 directly over T when the bomb strikes. The angle of depression at which T is sighted just as the bomb is released is P 1 PT .  

6. 6 The path, or trajectory of the bomb is arc PCT , a part of a parabola. If s feet is the vertical distance fallen by the bomb in t seconds, from physics we know that ; where g = 32.2 ft/sec 2     Note = 9.81 m/s 2  

7. 7                        

8. 8 Example 1. How long does a bomb take to fall 10000 feet?        

9. 9 Example 2. If an airplane at an elevation of 10000 ft drops a bomb while flying at a speed of 240 miles per hour, find the airplane’s ground distance from the target ( AT ).  

10. 10 Example 2. If an airplane at an elevation of 10000 ft drops a bomb while flying at a speed of 240 miles per hour, find the airplane’s ground distance from the target ( AT ).          

11. EXERCISE 5 Sketch an illustration of the following problems, with proper labels. Then, solve what is required in each problem. 11

12. Exercise 5A 12 An American flying fortress is preparing for bombing while flying horizontally at a speed of 200 miles per hour. Find: how long it takes a bomb to fall; the airplane’s ground distance from the target; the angle of depression at which the target should be sighted when the bombardier releases the bomb if the airplane is at the given elevation: