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ivann1987 [24]
3 years ago
10

Rockfalls can cause major damage to roads and infrastructure. To design mitigation bridges and barriers, engineers use the coeff

icient of restitution to model the behavior of the rocks. The rock A falls a distance of 32 m before striking an incline with slope α = 40°. Knowing that the coefficient of restitution between A and the incline is 0.2, determine the velocity of the rock after the impact.

Engineering
1 answer:
Rus_ich [418]3 years ago
5 0

Answer:

Velocity of rock fall collision, v = 13.21 m/sec

Explanation:

Detailed explanation given in the attached document.

You might be interested in
Use Routh's stability criterion to determine how many roots with positive real parts the following equations have:
Pavlova-9 [17]

Answer:

a) no roots not in LHP

b) 2 roots not in LHP

c) 2 roots not in the LHP

d) 2 roots not in the LHP

e) 2 roots not in LHP

Explanation:

a) s^4 + 8s^3 + 32s^2 + 80s + 100 = 0\\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:32\:\:\:\:\:\:100\\s^3:\:\:\:8\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:80\\s^2:\:\:\:22\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:100\\s^1:\:\:\:80-\frac{800}{22} =43.6\\s^0:\:\:\:100

No roots not in the LHP

b) s^5 + 10s^4 + 30s^3 + 80s^2+344s + 480 =0 \\\\s^5:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:30\:\:\:\:\:\:344\\s^4:\:\:\:10\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:480\\s^3:\:\:\:22\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:296\\s^2:\:\:\:-545\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:480\\s^1:\:\:\:490\\s^0:\:\:\:480

2 roots not in the LHP

c) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:7\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:8\\s^3:\:\:\:2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:-2\\s^2:\:\:\:8\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:8\\s^1:\:\:\:-4\\s^0:\:\:\:8

There are roots in the RHP (not all coefficients are greater than 0).

2 roots not in the LHP

d) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^3:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:20\\s^2:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:78\\s^1:\:\:\:-58\\s^0:\:\:\:78

There are two sign changes in the first column of the Routh array.

2 roots not in the LHP

e) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:25\\s^3:\:\:\:4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:12\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: new \:\:row \\s^2:\:\:\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:25\\s^1:\:\:\:12-\frac{100}{3}=-21.3 \\s^0:\:\:\:25

2 roots not in LHP

check:

 a (s) = 0  ⇒

 s^2 = -3 \limits^+_- 4j = 5e^{j(\pi \limits^+_- 0.92)}\\\\s = \sqrt5 e^{j( \frac{\pi}{2} \limits^+_-  0.46)+n\pi j},\:\:\:\:\: n= 0, 1\\

3 0
3 years ago
Consider a fully developed flow in a circular pipe (negligible entrance effects), how does the convective heat transfer coeffici
Alexeev081 [22]

Answer: A)  Gradually decrease

Explanation:

  The convection value of heat transfer rate are gradually decreasing with the flow of the heat. Flow in a circular pipe, flow direction does not change in the velocity path. The average of the coefficient of heat transfer and the number of pipes are needed and the effects are get neglected so that is why the flow are fully developed.

8 0
3 years ago
¿Como influye la alimentación en nuestro organismo?
ra1l [238]

Answer: Comer bien ayuda a reducir el riesgo de problemas de salud física como enfermedades cardíacas y diabetes. También ayuda con los patrones de sueño, los niveles de energía y su salud en general. Es posible que haya notado que su estado de ánimo a menudo afecta los tipos de alimentos que elige, así como la cantidad que come.

English Translation: Eating well helps to reduce the risk of physical health problems like heart disease and diabetes. It also helps with sleeping patterns, energy levels, and your general health. You may have noticed that your mood often affects the types of food you choose, as well as how much you eat.

7 0
3 years ago
The Air Force One (Boeing 747-200) has a long-range mission takeoff gross load 833,000 pounds (Ibm). What is Air Force One's tak
Ahat [919]

Answer:

The mass in:

1) Grams =377765.5\times 10^{3}grams

2) Kilograms =377765.5kilograms

3)Tonnes =377.7655tonnes

4) Megatonnes =0.378megatonnes

Explanation: The given mass of the aircraft in pounds is 833,000 pounds.

Part 1)

Since we know that 1 pound equals 453.5 grams thus by ratio we have

833,000 pounds =833000lb\times 453.5\frac{g}{lb}=377765.5\times 10^{3}grams

Part 2)

Since we know that 1000 grams equals 1 kilogram

thus the above mass in kilograms equals\frac{377765.5\times 10^{3}}{1000}=377765.5kg

Part 3)

Since there are 1000 kilograms in 1 tonne

thus the given mass is converted into tonnes as

mass_{tonnes}=\frac{377765.5kg}{1000}=377.765tonnes

Part 4)

Since 1 Mega tonne(Mton) equals 1000 tonnes thus the given mass is converted into mega tonnes as

mass_{M\cdot tonn}=\frac{377.7655tonnes}{1000}=0.378Megatonnes

4 0
4 years ago
Low relative humidity can cause wood furniture joints to swell​
olga2289 [7]

Answer:

yes

Explanation:

4 0
3 years ago
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