Respuesta :
Answer:
The terminal voltage is [tex]v_T = 90.76\ m/s[/tex]
Explanation:
From the question we are given that the Resistive force R is mathematically represented as
[tex]R = -bv[/tex]
Where b is a constant known as drag coefficient
v is the velocity of the object
The objective of this solution is to obtain the terminal speed and this is mathematically represented as
[tex]V_T = \frac{mg}{b}[/tex]
Where m is the mass
g acceleration due to gravity
As the time changes the velocity of the object change and this can be mathematically represented as
[tex]v = v_T[1-e^{bt/m}][/tex]
We are told that the [tex]v = \frac{1}{2} v_T \ at \ t = 6.56s[/tex]
So substituting this into the above equation we have
[tex]\frac{v_T}{2} = v_T [1-e^{bt/m}][/tex]
[tex]\frac{1}{2} = 1- e^{bt/m}[/tex]
[tex]e^{-(b*6.56)/m}= 1-\frac{1}{2}[/tex]
[tex]\frac{b}{m} = \frac{ln(2) }{6.56}[/tex]
Substituting m = 7.8 kg
[tex]b= \frac{ln(2)}{6.56} *7.8 =0.8242\ kg/m[/tex]
Now substituting this value to get the terminal velocity we have
[tex]v_T = \frac{7.8 * 9.8}{0.8422} =90.76\ m/s[/tex]
The terminal speed of the given object could be stated as:
[tex]90.76 m/s[/tex]
Given that,
R(Resistive Force) [tex]= -bv[/tex]
where [tex]b[/tex] being constant and [tex]v[/tex] represents the velocity
To find,
Terminal speed = ?
We will represent terminal speed as [tex]v_{T}[/tex].
so,
[tex]v_{T}[/tex] [tex]= mg/b[/tex]
where [tex]m[/tex] represents mass and
[tex]g[/tex] represents acceleration due to gravity.
With the alteration in time, the velocity varies as well. Therefore,
[tex]v_{T}/2 = v_{T}[1 - e^{bt/m}][/tex]
As we know,
[tex]v = 1/2v_{T}[/tex] and t = 6.56s
After putting these values in [tex]v_{T}/2 = v_{T}[1 - e^{bt/m}][/tex], we get
[tex]b = \frac{In(2)}{6.56}[/tex] × [tex]7.8[/tex]
[tex]= 0.8242 kg/m[/tex]
After this, we will put b's value in the former equation,
[tex]v_{T}[/tex] [tex]= (7.8[/tex] × [tex]9.8)/0.8242[/tex]
∵ [tex]v_{T}[/tex] [tex]= 90.76 m/s[/tex]
Thus, [tex]90.76 m/s[/tex] would be characterized as the terminal speed.
Learn more about "Terminal Speed" here:
brainly.com/question/7570550
