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Answer:
δL/δt = 634,38 ft/s
Step-by-step explanation:
A right triangle is shaped by ( y = distance between aircraft and ground which is constant and equal to 405 f ) a person who is at ground level 3040 f away from the tower distance x = 3040 f and the line between the aircraft and the person. Then we can use Pythagoras theorem and write
L ( distance between aircraft and person )
L² = x² + y² or L² = x² + (405)²
Taken partial derivatives with respect to t we get:
2*L*δL/δt = 2*x*δx/t + 0
Then L*δL/δt = x*δx/dt
At the moment of the aircraft passing over the tower
x = 3040 ft δx/δt = 640 ft/s and L = √ ( 3040)² + (405)²
So L = √9241600 + 164025 L = √9405625 L ≈3066,9 ft
Then:
δL/δt = 3040*640/ 3066,9 units [ ft * ft/s / ft ] ft/s
δL/δt = 634,38 ft/s
The prism has 6 faces: 2(length·width), 2(length·heighth), & 2(width·heighth)
2(length · width) = 2(9.8 · 20) = 2(196) = 392 in²
2(length · heighth) = 2(9.8 · 5) = 2(49) = 98 in²
2(width · heighth) = 2(20 · 5) = 2(100) = 200 in²
The sum of the faces is the surface area (S.A.)
392 in² + 98 in² + 200 in² = 690 in²
-8x-3(4x-y)+7y
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