A train travels 79 kilometers in 2 hours, and then 77 kilometers in 3 hours. What is its average speed?
1 answer:
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Answer:
The air temperature at the tropopause is - 79 °C
Explanation:
We know that a station near the equator has a surface temperature of 25°C
Vertical soundings reveal an environmental lapse rate of 6.5 °C per kilometer.
The tropopause is encountered at 16 km.
In order to find the air temperature at the tropopause we are going to deduce a linear function for the temperature at the tropopause.
This linear function will have the following structure :
Where '''' and ''
'' are real numbers.
Let's write to denote the temperature '' T '' in function of the distance
'' x '' ⇒
We can reorder the function as :
(I)
Now, at the surface the value of '''' is 0 km and the temperature is 25°C so in the function (I) we write :
⇒
⇒
(II)
In (II) the value of '''' represents the change in temperature per kilometer.
Because the temperature decrease with the height this number will be negative and also a data from the question ⇒
(III)
In (III) we deduced the linear equation. The last step is to replace by in (III) ⇒
The air temperature at the tropopause is - 79 °C
The tension in the rope when the gymnast climbs it at constant speed is 641.9 N.
Given:
Mass of gymnast, m = 65.5 kg
The speed 'v' of gymnast is constant
Solution:
Consider the free-body diagram of the system as shown below.
Balancing forces along the vertical axis we get:
ΣFy = 0
Thus, we get:
F = ma - (1)
where, m is mass of gymnast
a is acceleration of gymnast (a = 0m/s², as the speed is constant)
Also,
F = T - mg -(2)
where, T is tension in the rope
g is acceleration due to gravity
Equating (1) & (2), we get:
ma = T - mg
Re-arranging the equation, we get:
T = m(a+g)
Applying values in above equation we get:
T = (65.5 kg)(0 m/s²+9.8 m/s²)
T = 641.9 N
Therefore, the tension in the rope when the gymnast climbs it at constant speed is 641.9 N.
Learn more about tension here:
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