Answer: B) 14.7 meters
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Explanation:
The bottle cap is a projectile, so we'll use the aptly named projectile formula
That formula (the meters version of it anyway) is approximately
h = -4.9t^2 + v*t + s
where,
t = elapsed time in secondsh = height at time tv = starting velocitys = starting heightWe'll assume that s = 0, though realistically it's probably going to be a bit larger than this (since the person is holding it above the ground). For the sake of simplicity, we'll stick with s = 0.
We're told that the initial velocity is 17 m/s, which means v = 17.
All of that means the formula mentioned earlier updates into this:
h = -4.9t^2 + 17t
If we were to graph this, or apply the -b/(2a) formula, then you should find that the vertex occurs when t = 1.73469 approximately.
Plug this into the equation we found to get...
h = -4.9t^2 + 17t
h = -4.9(1.73469)^2 + 17(1.73469)
h = 14.7449
h = 14.7
The bottle cap will reach a peak height of approximately 14.7 meters and does so at around the 1.7 second mark. The total flight time is approximately 2*1.7 = 3.4 seconds. This all assumes that the starting height and ending height are both 0 meters off the ground.
The soda will go as high as 14.7 meters. Therefore, option (B) is correct.
What is the conservation of energy principle?We can solve this problem using the conservation of energy principle, which states that the initial energy of a system is equal to the final energy. At the start, the soda in the bottle has some potential energy due to its position and kinetic energy due to its motion. When the soda shoots out of the bottle, it converts all of its initial energy to potential energy as it reaches its maximum height.
Using the conservation of energy, we can write:
Initial energy = Final energy
[tex]0.5 * m * v^2 = m * g * h[/tex]
where m is the mass of the soda, v is its velocity, g is the acceleration due to gravity ([tex]9.8 m/s^2[/tex]), and h is the height it reaches.
Solving for h, we get:
h = [tex](v^2)/(2g) = (17^2)/(29.8)[/tex]= 14.7 m
Therefore, the soda will go as high as 14.7 meters. Option B is correct.
Learn more about the conservation of energy principle, here:
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The length, breadth and height of a box is 50cm, 20cm and 10cm respectively then find surface area of its base and volume.
I just hope this pic will help you
Driving home from school one day, you spot a ball rolling out into the street . (See the figure below) You brake for 1.50 s , slowing your 950-kg car from 16.0 m/s to 9.50 m/s.
a)What was the magnitude of the average force exerted on your car during braking?
b)What was the direction of the average force exerted on your car during braking?
c)How far did you travel while braking?
Answer:
a) 4116.67 N
b) negative (assuming car is traveling in positive direction)
c) 19.125 m
Explanation:
Part A)We can find the average force exerted on the car by using Newton's 2nd Law: F = ma.
We have the mass (950 kg) but we do not have the acceleration. Let's solve for this using kinematics.
We have the time during braking, the initial and final velocity, and we need to find the acceleration. To do this, we can use the following equation: v = v₀ + at.
v (final velocity) = 9.50 m/sv₀ (initial velocity) = 16.0 m/st (time) = 1.50 s a = ?Substitute these values into the equation.
v = v₀ + at9.50 m/s = 16.0 m/s + a (1.50 s) 9.50 = 16.0 + 1.50a -6.50 = 1.50a a = -4.333333... m/s²The car's acceleration during the braking period is -4.33 m/s², assuming the car is traveling in the positive direction.
Now, we can use this to plug into Newton's 2nd Law to find the force exerted on the car.
F = maF = (950 kg) (-4.33...) F = -4116.666667 NThe magnitude of the average force exerted on the car while braking is the absolute value, so it is 4116.67 N.
Part B)The direction of the average force is denoted in the negative sign. It is opposite the direction of the car's motion. Assuming that the car is traveling in the positive direction, the direction of the average force exerted on the car is in the negative direction since this force is slowing the car down while braking.
Part C)We can find the distance traveled during the braking period by using another kinematic equation.
We have the initial and final velocity, and the time traveled, so we can use this equation: Δx = v_avg · t.
Note that v_avg is the same thing as (v + v₀) / 2.Substitute the known values into the equation.
Δx = [(9.50 + 16.0)/2] · 1.50 Δx = 12.75 · 1.50Δx = 19.125 mThe car traveled 19.125 m while braking.
What is the amount of force exerted by gas particles?
Answer:
Pressure is the force divided by the area on which the force is exerted, and temperature is measured with a thermometer. We gain a better understanding of pressure and temperature from the kinetic theory of gases, which assumes that atoms and molecules are in continuous random motion.
A positively charged glass rod is bought close to a suspended metal needle. What
can we say about the charge on the needle given that the needle is
a) attracted ?
b) repelled ?
Answer:
attracted
Explanation:
opposite charges attract each other when the rub against each other
Answer:
This depends because the electrostatic force obeys the principle that states that force between both of the particles does not get affected by the charges of the other thus if the needle is getting attracted it possess negative charges( the opposite charge) .And if they repel it means they have the same charges ( positive charges).
Which of the following is NOT an important phenomenon that commonly erodes and weathers exposed rock outcrops to form sedimentary material?
a) Lightning
b) Wind
c) Rain
d) Freezing/Thawing
Answer:
Explanation:
While each of these can cause erosion and weathering, lightning is probably the least important as it occurs less frequently and affects a much smaller surface area when it strikes.
Wind is not very effective by itself, but it can carry abrasives which work to degrade rock surfaces. It covers a very large area at once so the net effect can be moderate to large especially desert areas where plants are not readily available to disrupt the flow.
Rain covers huge areas and is quite common.
Freezing/Thawing cycles cover large areas and are quite common in the temperate and arctic latitudes and even in tropical altitudes.
Attached is a photo taken atop Half Dome in Yosemite National Park showing two of thousands of divots in the rock there caused by lightning strikes. The current in the lightning heats the stone causing water trapped in it to flash to steam. The increased pressure inside the stone can overwhelm the material strength and blow rock chunks over a fairly good sized area. This is a fairly rapid weathering and erosion when it occurs, but that is typically limited to a few dozen days per year and occurs mostly on high ground where lightning is more likely to strike earth.
60.96-mile distance in kilometers
Answer:
98.105610 Kilometers
Explanation:
Rounded to 8 digits
Answer:
98.11 km
Explanation:
60.96 mi (5280ft/mi)(12 in/ft)(2.54 cm/in)(1 m/ 100cm)(1 km/1000 m) = 98.10561024 km
however, reporting this precision to the nearest hundred millionth of a kilometer is silly as we only know the mile dimension to the nearest hundredth of a mile.
A hundredth of a mile is 5280/100 = 52.8 ft or just over 16 m
It would only be a little bit of a presumption to give our precision to the nearest 10 meters as I have done.
This also fits neatly into the significant digits rule. Both the original dimension and the converted dimension have four significant digits.
9.1 x 105 – 7.2 x 105
=
Answer:
1.9 x 10⁵
Explanation:
I ASSUME your question is supposed to read
9.1 x 10⁵ – 7.2 x 10⁵ =
9.1 - 7.2 = 1.9 and the powers are the same so just tag them along
its the same as
910000 - 720000 = 190000
1.9 x 105 could be another possibility if the question is actually posed correctly.
Name another way that energy is made
Answer:
The three major categories of energy for electricity generation are fossil fuels (coal, natural gas, and petroleum), nuclear energy, and renewable energy sources. Most electricity is generated with steam turbines using fossil fuels, nuclear, biomass, geothermal, and solar thermal energy.
Explanation:
Solar
Wind
Geothermal
Hydrogen
TidaWave
Hydroelectric
Biomass
