Answer:
Explanation:
Given data:
Weight W = 16 lb
length l = 6/12 = 0.5 ft
hence, spring constant k = W/l = 16/0.5 = 32 lb/ft
The equation of motion of spring is
the auxiliary equation can be written as
The discriminate of equation is
To get the value of the damping constant,
Answer:
The length of his shadow is decreasing at a rate of 0.9375 m/s
Explanation:
An image of this scenario is presented in the attached file to this solution. The image shows the exact moment when the 2m tall man is 4m away from the building.
First of, when the man is 4m away from the building, he is 8m away from the spotlight,
Using the concept of similar triangles, we can obtain the value of y at this point.
(8/2) = (12/y)
y = 3 m when the man is 8 m away from the spotlight.
From the image,
But generally, for x and y at any point,
(x/2) = (12/y)
xy = 24
Differentiating with respect to t
(d/dt)(xy) = (d/dt)12
y (dx/dt) + x (dy/dt) = 0
x (dy/dt) = - y (dx/dt)
At x = 8m, y = 3m, (dx/dt) = 2.5 m/s
8 (dy/dt) = - 3 (2.5)
(dy/dt) = - 7.5/8 = - 0.9375 m/s
The minus sign indicates that the height of the shadow decreases as the man moves towards the wall.
Hope this Helps!!!
With the below stated fact I think that the pros of using synthetic materials outweighs the cons.
Before we answer the question
If the pros of using synthetic materials outweigh the cons or otherwise, let us first establish the what a synthetic material is and its pros and cons
Synthetic material
Synthetic material is a material in which a substances are changed chemically to produce a material with different characteristics.
Types of Synthetic material
- Plastic bag
- Synthetic fiber/cloth
- Artificial sweetener
- Synthetic fuel
- Aspirin
Pros of Synthetic materials
- They are used in construction because of there strong bonding
- They can be molded
- They can be colored into any shade
- They are cheap
Cons of Synthetic materials
- Sometimes none degradable
- They do not absorb water.
- They are highly flammable
- Melts easily
In conclusion
Although Synthetic materials has so very pressing disadvantages to human kind it is unrefusable the importance of Synthetic materials to the day to day live of all humans
Therefore, I think that the pros of using synthetic materials outweighs the cons
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