Explanation:
Given formula:
ME=
mv²+mgh
To make height the subject of the formula, follow the following procedures;
Subtract mv² from both side of equation
M.E - mv² = mv² - mv²+mgh
This gives:
M.E - mv² = mgh
Multiply both sides of the expression by 
( M.E - mv² ) x = x mgh
h = ( M.E - mv² ) x
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Answer:
In a coiled spring, the particles of the medium vibrate to and fro about their mean positions at an angle of
A. 0° to the direction of propagation of wave
Explanation:
The waveform of a coiled spring is a longitudinal wave, which is made up of vibrations of the spring which are in the same direction as the direction of the wave's advancement
As the coiled spring experiences a compression force and is then released, it experiences a sequential movement of the wave of the compression that extends the length of the coiled spring which is then followed by a stretched section of the coiled spring in a repeatedly such that the direction of vibration of particles of the coiled is parallel to direction of motion of the wave
From which we have that the angle between the direction of vibration of the particles of the coiled spring and the direction of propagation of the wave is 0°.
The optimal angle of 45° for maximum horizontal range is only valid when initial height is the same as final height.
<span>In that particular situation, you can prove it like this: </span>
<span>initial velocity is Vo </span>
<span>launch angle is α </span>
<span>initial vertical velocity is </span>
<span>Vv = Vo×sin(α) </span>
<span>horizontal velocity is </span>
<span>Vh = Vo×cos(α) </span>
<span>total time in the air is the the time it needs to fall back to a height of 0 m, so </span>
<span>d = v×t + a×t²/2 </span>
<span>where </span>
<span>d = distance = 0 m </span>
<span>v = initial vertical velocity = Vv = Vo×sin(α) </span>
<span>t = time = ? </span>
<span>a = acceleration by gravity = g (= -9.8 m/s²) </span>
<span>so </span>
<span>0 = Vo×sin(α)×t + g×t²/2 </span>
<span>0 = (Vo×sin(α) + g×t/2)×t </span>
<span>t = 0 (obviously, the projectile is at height 0 m at time = 0s) </span>
<span>or </span>
<span>Vo×sin(α) + g×t/2 = 0 </span>
<span>t = -2×Vo×sin(α)/g </span>
<span>Now look at the horizontal range. </span>
<span>r = v × t </span>
<span>where </span>
<span>r = horizontal range = ? </span>
<span>v = horizontal velocity = Vh = Vo×cos(α) </span>
<span>t = time = -2×Vo×sin(α)/g </span>
<span>so </span>
<span>r = (Vo×cos(α)) × (-2×Vo×sin(α)/g) </span>
<span>r = -(Vo)²×sin(2α)/g </span>
<span>To find the extreme values of r (minimum or maximum) with variable α, you must find the first derivative of r with respect to α, and set it equal to 0. </span>
<span>dr/dα = d[-(Vo)²×sin(2α)/g] / dα </span>
<span>dr/dα = -(Vo)²/g × d[sin(2α)] / dα </span>
<span>dr/dα = -(Vo)²/g × cos(2α) × d(2α) / dα </span>
<span>dr/dα = -2 × (Vo)² × cos(2α) / g </span>
<span>Vo and g are constants ≠ 0, so the only way for dr/dα to become 0 is when </span>
<span>cos(2α) = 0 </span>
<span>2α = 90° </span>
<span>α = 45° </span>
1. electrical energy: electrical energy that is caused by moving electrons
2. coolant: a mixture of antifreeze and water that removes excess heat from an internal engine
3. electric compressor: a device that <span>acts as a pump, circulating refrigerant throughout the refrigerator
4. the inside of the fridge and the food becomes colder
5. the coolants becomes a hot, high-pressure gas
6. as coolant transfers thermal energy to the air outside, it turns back into a liquid
</span>
Answer:
We use electrolysis to prevent a material from rusting,
The metal forms a coating around the material and hence prevents any contact between the material and the environment
This process also gives us the physical strength of the material and the aesthetic properties of the coated metal
the metal commonly used to coat the object is Zinc and the process is called galvanisation
