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The key to this question lies in the information within the bracket. Some things you must understand before you answer this question are, 1. Energy cannot be created or destroyed, it can only be transferred 2. Kinetic energy stores and GPE stores. 

What do I mean by point 1. Well if energy could be created or destroyed, we would never know how much energy the car has at the bottom! The second thing you need to understand is that when it is at the top of the slope, it is at a height and so will have GPE. How much you ask? Well you can work it out using the formula GPE = mgh. In this question they haven't given us the mass and you will see why soon.

Next, you must know that KE depends on the speed of the car. The higher the speed, the higher the kinetic energy. Now you must think where does it get this kinetic energy from? Is there anyone applying a force after it has started rolling? NO! When it starts rolling down, the gpe is being CONVERTED into ke.  How much of it is converted? All of it!
Therefore, if GPE = KE then we can say mgh=½mv². Finally we can work out the speed which in this equation is v. If we multiply both sides by 2 we get 2mgh=mv². Now if we divide both sides by m, we get 2gh= v². Can you see there is no m left in the equation. That means the velocity at the bottom of the ramp doesn't depend on the mass! You can check this yourself by sliding a car down a ramp, and adding weights on. You should notice the speed remains roughly the same. Now finally back to the equation, if we share root both side, we end up with v=sqrt(2gh) (g on earth is 9.81). Now if we substitute h as 2 then we get an answer of 6.26 meters per second. 

I understand that was a very long explanation but if you understood everything above, you are close to mastering this topic! I hope you found this helpful and I am willing to answer any question you may have.

11+ Entrance Exams

A toy car slides down a slope. If the top of the slope is 2m higher than the foot of the slope, how fast will the car be moving when it reaches the foot? (Assume that all of its g.p.e is transformed to k.e

Conservation of e

Although you can do this by expansion alone, it would be much easier to use binomial expansion. In this case, the bracket is being raised to the power of four and so the coefficients will be 1,4,6,4,1. One important thing to note is the -Y, which will make the signs in our expansion oscillate. We also know that the X will be raised to the power of four in the first term and decrease by one every time, so it will go X^4 then X cubed, X squared... Similarly, the (-Y) will go up starting from 0 as (-Y)^0, (-Y)^1... all the way up to 4. So our first term will be 1*(X)^4*(-Y)^0 which is just X^4. Then the second term will be 4*(X)^3*(-Y)^1 and so on. The complete binomial expansion will look like this:  

1*(X)^4*(-Y)^0 + 4*(X)^3*(-Y)^1 + 6*(X)^2*(-Y)^2 + 4*(X)^1*(-Y)^3 + 1*(X)^0*(-Y)^4.

Simplifying should give you 

X^4 - 4YX^3 + 6X^2 Y^2 - 4XY^3 +Y^4

Maths

Find each product            (X-Y)^4

The sum of the inner angles in a trapezium will always be 360°. This is because it has 4 sides. This comes from the basis that the sum of inner angles in a triangle add up to 180°.
If you draw a line from one corner of a quadrilateral to the opposite corner, you can see two triangles. Therefore you multiply 180 by 2. 
If you have any other shape with sides n, you can work out the number of triangles that will fit by doing n-2. So a shape with sides n will have inner angles that add up to 180×(n-2).

How do I find out what the sum of the inner angle of a trapezium?

Most of the people who have died due to coronavirus or Covid-19 had an underlying health condition which weakened their immune system. Compared to SARS covid-19, has a longer incubation period with 7 days before symptoms appear. SARS on the other hand was 2-7 days. Looking at the death rate for covid-19 it can be said that it is less severe. However, it is more contagious due to the longer incubation period because you will be infecting more people before you can self isolate.

Biology

Was SARS as dangerous as Corona virus?

The energy rating of an appliance tells you how efficient it is. You may see stickers that have a tower of letters with the more efficient ones labeled A, A+, and less efficient ones as C or D. They tell you how much of the energy you supply is used usefully. For example, you may supply a kettle with 100J of energy of which 15J is used to heat up the water. The other 85J may be used as sound or for heating the surroundings in other words wasted. Another kettle might also be supplied 100J from which it might use 90J to heat up the water. As you can see the latter uses the energy more efficiently and so will have a higher energy rating. Energy rating can also be thought of as power since power tells you the rate of energy transfer.

How do you calculate the energy rating of an appliance

Applying for Medicine

This is a quesiton

To find the area of ANY quadrilateral, you need to split it up into two triangles, work out their areas individually and add them up.
Doing this with recognisable shapes like a square is where we get the formula. Area of a square is the length of one side squared, rectangle is base×height etc. If you identify the shape, it will be much easier to work out the area using the formula but if it is an irregular quadrilateral then the method above will always work. 

How to calculate the area of ​​any quadrilateral

An obtuse angle is defined as greater than 90° and a triangle must have angles that add up to exactly 180°, nothing more or less. So if you have two angles that are obtuse, they will always add up to more than 180 making the third angle impossible. Therefore Laura is correct

Laura thinks that a triangle cannot have two obtuse angles.Do you agree? Explain your answer.

You should rearrange the second equation for either x or y, both ways will work. If y=2-x, then change all the y's in the first equation to 2-x and simplify. You should have a quadratic which when you solve will give you two x values. Using those you can work out the corresponding y values using x+y=2

How do you solve the simultaneous equations xsquared + ysquared =9 and  x+y=2

For past papers and mark schemes, www.physicsandmathstutor.com is really good, for most subjects they even have questions split by topic. So if you wanted to practice questions on a particular area, there will be a pack with just those questions. Of course, there are more subjects than just Maths and Physics despite the name of the website.

Awais Naveed

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