The initial velocity of the ball is 1.01 m/s
Explanation:
The motion of the ball rolling off the desk is a projectile motion, which consists of two independent motions:
- A uniform horizontal motion with constant horizontal velocity
- A vertical accelerated motion with constant acceleration (
, acceleration due to gravity)
We start by analyzing the vertical motion: we can find the time of flight of the ball by using the following suvat equation

where
s = 1.20 m is the vertical displacement (the height of the desk)
u = 0 is the initial vertical velocity

t is the time of flight
Solving for t,

Now we analyze the horizontal motion. We know that the ball covers a horizontal distance of
d = 0.50 m
in a time
t = 0.495 s
Therefore, since the horizontal velocity is constant, we can calculate it as

So, the ball rolls off the table at 1.01 m/s.
Learn more about projectile motion:
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Potential energy behind dams
Answer: Hi!
A terrestrial planet is composed of a solid substance like rock or earth. A few examples are our planet, Earth, and the red planet, Mars. These are the planets that are the closest to the sun. There are four terrestrial planets in total. The only known terrestrial planet that has life, however, is our own, Earth! Earth has the perfect conditions for supporting life forms.
Hope this helps!
<h2>
Answer:</h2>
In circuits, the average power is defined as the average of the instantaneous power over one period. The instantaneous power can be found as:

So the average power is:

But:

So:

![P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}(\frac{1+cos(2\omega t)}{2} )dt \\\\P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}[\frac{1}{2}+\frac{cos(2\omega t)}{2}]dt \\\\P=\frac{v_{m}i_{m}}{T}[\frac{1}{2}(t)\right|_0^T +\frac{sin(2\omega t)}{4\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2T}[(t)\right|_0^T +\frac{sin(2\omega t)}{2\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7Bv_%7Bm%7Di_%7Bm%7D%7D%7BT%7D%5Cintop_%7B0%7D%5E%7BT%7D%28%5Cfrac%7B1%2Bcos%282%5Comega%20t%29%7D%7B2%7D%20%29dt%20%5C%5C%5C%5CP%3D%5Cfrac%7Bv_%7Bm%7Di_%7Bm%7D%7D%7BT%7D%5Cintop_%7B0%7D%5E%7BT%7D%5B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7Bcos%282%5Comega%20t%29%7D%7B2%7D%5Ddt%20%5C%5C%5C%5CP%3D%5Cfrac%7Bv_%7Bm%7Di_%7Bm%7D%7D%7BT%7D%5B%5Cfrac%7B1%7D%7B2%7D%28t%29%5Cright%7C_0%5ET%20%2B%5Cfrac%7Bsin%282%5Comega%20t%29%7D%7B4%5Comega%7D%20%5Cright%7C_0%5ET%5D%20%5C%5C%20%5C%5C%20P%3D%5Cfrac%7Bv_%7Bm%7Di_%7Bm%7D%7D%7B2T%7D%5B%28t%29%5Cright%7C_0%5ET%20%2B%5Cfrac%7Bsin%282%5Comega%20t%29%7D%7B2%5Comega%7D%20%5Cright%7C_0%5ET%5D%20%5C%5C%20%5C%5C%20P%3D%5Cfrac%7Bv_%7Bm%7Di_%7Bm%7D%7D%7B2%7D)
In terms of RMS values:
