Answer:
High ceilings make a room feel large and open, but they can be difficult to cool and heat. Because hot air rises, the challenge becomes trying to keep the hot air where you want it and preventing if from being wasted where you don't.
Explanation:
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Answer:
4.5 s, 324 ft
Explanation:
The object is projected upward with an initial velocity of

The equation that describes its height at time t is
(1)
where t, the time, is measured in seconds.
In order to find the time it takes for the object to reach the maximum height, we must find an expression for its velocity at time t, which can be found by calculating the derivative of the position, s(t):
(2)
At the maximum heigth, the vertical velocity is zero:
v(t) = 0
Substituting into the equation above, we find the corresponding time at which the object reaches the maximum height:

And by substituting this value into eq.(1), we also find the maximum height:

Magnitude of the force of tension: 139 N
Explanation:
The surface of the ramp here is assumed to be the positive x-direction.
To solve this problem and find the magnitude of the force of tension, we have to analyze only the situation along the x-direction, since the force of tension lie in this direction.
There are three forces acting along the x-direction:
- The force of tension,
, acting up along the plane - The force of friction,
, acting down along the plane - The component of the weight in the x-direction,
, acting down along the plane
We know that the magnitude of the weight is

So its x-component is

The net force along the x-direction can be written as

And therefore, since the net force is 98 N, we can find the magnitude of the force of tension:

Learn more about inclined planes:
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Explanation:
The given data is as follows.
Spring constant (k) = 78 N/m, 
Mass of block (m) = 0.50 kg
According to the formula of energy conservation,
mgh sin
h =
= 
= 0.64 m
Thus, we can conclude that the distance traveled by the block is 0.64 m.