As soon as I saw the beginning of the question, I knew that
when I opened it and read the rest, there would be no graphs
to rank. I was not disappointed.
Answer:74.33 feet per sec
Explanation:
Given
Police car is 50 feet side of road
Red car is 140 feet up the road
Distance between them is decreasing at the rate of 70 feet per sec
From figure
![x^2+y^2=z^2](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3Dz%5E2)
![z=\sqrt{140^2+50^2}](https://tex.z-dn.net/?f=z%3D%5Csqrt%7B140%5E2%2B50%5E2%7D)
z=148.66 feet
as the red car is moving
therefore its velocity magnitude is given by
![\frac{\mathrm{d} x}{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![2x\times \frac{\mathrm{d} x}{\mathrm{d} t}+0=2z\frac{\mathrm{d} z}{\mathrm{d} t}](https://tex.z-dn.net/?f=2x%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%2B0%3D2z%5Cfrac%7B%5Cmathrm%7Bd%7D%20z%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![x\frac{\mathrm{d} x}{\mathrm{d} t}=z\frac{\mathrm{d} z}{\mathrm{d} t}](https://tex.z-dn.net/?f=x%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3Dz%5Cfrac%7B%5Cmathrm%7Bd%7D%20z%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![140\times \frac{\mathrm{d} x}{\mathrm{d} t}=148.66\times 70](https://tex.z-dn.net/?f=140%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D148.66%5Ctimes%2070)
![\frac{\mathrm{d} x}{\mathrm{d} t}=74.33 feet\ per\ sec](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D74.33%20feet%5C%20per%5C%20sec)
Answer:
0.47 J
Explanation:
The elastic potential energy of a spring is given as,
E = 1/2ke²........................ Equation 1
Where E = Elastic potential energy, k = spring constant, e = extension/compression.
Given: k = 15 N/m, e = 0.25 m.
Substitute into equation 1.
E = 1/2(15)(0.25)²
E = 0.46875
E ≈ 0.47 J.
Hence the elastic potential energy stored in the spring = 0.47 J
I think they can use more durable materials.