The linear speed of the ladybug is 4.1 m/s
Explanation:
First of all, we need to find the angular speed of the lady bug. This is given by:
![\omega=\frac{2\pi}{T}](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B2%5Cpi%7D%7BT%7D)
where
T is the period of revolution
The period of revolution is the time taken by the ladybug to complete one revolution: in this case, since it does 1 revolution every second, the period is 1 second:
T = 1 s
Therefore, the angular speed is
![\omega=\frac{2\pi}{1 s}=6.28 rad/s](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B2%5Cpi%7D%7B1%20s%7D%3D6.28%20rad%2Fs)
Now we can find the linear speed of the ladybug, which is given by
![v=\omega r](https://tex.z-dn.net/?f=v%3D%5Comega%20r)
where:
is the angular speed
r = 65.0 cm = 0.65 m is the distance of the ladybug from the axis of rotation
Substituting, we find
![v=(6.28)(0.65)=4.1 m/s](https://tex.z-dn.net/?f=v%3D%286.28%29%280.65%29%3D4.1%20m%2Fs)
Learn more about angular speed:
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Check the attached file for the solution for this problem.
Answer:
Explanation:
Chemical properties only manifest when a chemical reaction occurs. Being reactive, flammable and explosive are chemical properties, because they involve chemical reactions: the substances are changed; the chemical bonds of some substances, called reactants, are broken, and the chemical bonds are created, forming other substances, called products.
Solubility is a<em> physical property</em> because during dissolution no new substances are formed. You can prove it when the solvent evaporates leaving behind the same original substance.
The the observation that the substance is <em>soluble</em> is describing a <em>physical property.</em>
Answer:
2.47 m
Explanation:
Let's calculate first the time it takes for the ball to cover the horizontal distance that separates the starting point from the crossbar of d = 52 m.
The horizontal velocity of the ball is constant:
![v_x = v cos \theta = (25)(cos 35.9^{\circ})=20.3 m/s](https://tex.z-dn.net/?f=v_x%20%3D%20v%20cos%20%5Ctheta%20%3D%20%2825%29%28cos%2035.9%5E%7B%5Ccirc%7D%29%3D20.3%20m%2Fs)
and the time taken to cover the horizontal distance d is
![t=\frac{d}{v_x}=\frac{52}{20.3}=2.56 s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7Bv_x%7D%3D%5Cfrac%7B52%7D%7B20.3%7D%3D2.56%20s)
So this is the time the ball takes to reach the horizontal position of the crossbar.
The vertical position of the ball at time t is given by
![y=u_y t - \frac{1}{2}gt^2](https://tex.z-dn.net/?f=y%3Du_y%20t%20-%20%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
where
is the initial vertical velocity
g = 9.8 m/s^2 is the acceleration of gravity
And substituting t = 2.56 s, we find the vertical position of the ball when it is above the crossbar:
![y=(14.7)(2.56) - \frac{1}{2}(9.8)(2.56)^2=5.52 m](https://tex.z-dn.net/?f=y%3D%2814.7%29%282.56%29%20-%20%5Cfrac%7B1%7D%7B2%7D%289.8%29%282.56%29%5E2%3D5.52%20m)
The height of the crossbar is h = 3.05 m, so the ball passes
![h' = 5.52- 3.05 = 2.47 m](https://tex.z-dn.net/?f=h%27%20%3D%205.52-%203.05%20%3D%202.47%20m)
above the crossbar.