Answer:
100 J, 225 J
Explanation:
The kinetic energy of an object is given by:
where
m is the mass of the object
v is the velocity of the object
In this problem, the initial kinetic energy of the object is
K = 25 J
Then, the velocity is doubled, which means
v' = 2v
Therefore, the new kinetic energy will be
Therefore, the kinetic energy has quadrupled:
Later, the velocity is tripled, which means
v'' = 3v
Therefore, the new kinetic energy will be
Therefore, the kinetic energy has increased by a factor of 9:
This should help look at the pictures?
<span>f(x) = 5.05*sin(x*pi/12) + 5.15
First, you need to determine the period of the function. The period will be the time interval between identical points on the sinusoidal function. For this problem, the tide is rising and at 5.15 at midnight for two consecutive days. So the period is 24 hours. Over that 24 hour period, we want the parameter passed to sine to range from 0 to 2*pi. So the scale factor for x will be 2*pi/24 = pi/12 which is approximately 0.261799388. The next thing to note is the magnitude of the wave. That will simply be the difference between the maximum and minimum values. So 10.2 ft - 0.1 ft = 10.1 ft. And since the value of sine ranges from -1 to 1, we need to divide that magnitude by 2, so 10.1 ft / 2 = 5.05 ft.
So our function at this point looks like
f(x) = 5.05*sin(x*pi/12)
But the above function ranges in value from -5.05 to 5.05. So we need to add a bias to it in order to make the low value equal to 0.1. So 0.1 = X - 5.05, 0.1 + 5.05 = X, 5.15 = X. So our function now looks like:
f(x) = 5.05*sin(x*pi/12) + 5.15
The final thing that might have been needed would have been a phase correction. With this problem, we don't need a phase correction since at X = 0 (midnight), the value of X*pi/12 = 0, and the sine of 0 is 0, so the value of the equation is 5.15 which matches the given value of 5.15. But if the problem had been slightly different and the height of the tide at midnight has been something like 7 feet, then we would have had to calculate a phase shift value for the function and add that constant to the parameter being passed into sine, making the function look like:
f(x) = 5.05*sin(x*pi/12 + C) + 5.15
where
C = Phase correction offset.
But we don't need it for this problem, so the answer is:
f(x) = 5.05*sin(x*pi/12) + 5.15
Note: The above solution assumes that angles are being measured in radians. If you're using degrees, then instead of multiplying x by 2*pi/24 = pi/12, you need to multiply by 360/24 = 15 instead, giving f(x) = 5.05*sin(x*15) + 5.15</span>
Explanation:
1. Phases of Venus: Galileo was the first astronomer to use a telescope to observe the celestial objects. Through a telescope he observed that Venus shows the phases just like the Moon. This proved the Heliocentric theory correct against the then prevalent Geocentric theory.
2. Law of Falling bodies: The acceleration due to gravity is independent of weight of the objects that means two bodies of different mass will hit the ground at the same time if dropped from the same height.
3. The uneven surface of the Moon: He observed that the surface of the Moon is uneven and rough.
4. Discovery of the 4 Moons of Jupiter
