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Monisha (Student) December 8 2016
Jo (Parent) February 15 2017
Freyja (Student) December 15 2016
Jo (Parent) January 11 2017
This question is simply a matter of finding and applying the correct equation of motion.
First, draw a diagram - even if the situation in the questions seems really simple, it's always useful to draw a diagram.
The card is being dropped from rest; as the only force acting on it is gravity, the acceleration - and therefore final velocity - will be purely vertical. The question also specifies that the card is dropped from a given vertical distance - this is all good news as we will not have to resolve anything into horizontal and vertical components.
Now we write down all the quantities that we might find in an equation of motion that relate to the question.
s = distance travelled = 0.75m
u = initial velocity = 0 m/s
v = final velocity = 3.84 m/s
a = acceleration = g, to be found
t = time elapsed. We are not given t, nor are we at any point required to find it - so as far as we are concerned t is irrelevant!
The only quantities that matter are s, u, v and a; so we just find the equation of motion that includes these four, and substitute our values in.
From either memory or the formula sheet, we have the equation:
v2 - u2 = 2as.
Simply rearrange in terms of the value we are trying to find, in this case a, and plug in the numbers to get our estimate for g,
a = 9.83 m/s2.
You might notice this is actually slightly different from the accepted value of 9.81 - this is fine! The exam board will rarely have you calculate a known constant that comes out exactly right; this is to prevent you just looking up the answer in the formula booklet. As our answer is very close, we can be confident that the calculations are correct.see more
We start with £800 in the bank. As we are earning compound interest, it means that each year we get 3.5% of the original £800, plus 3.5% of any interest that has already been earned. So, at the end of the year, you will have
1.035 x (however much money was in the account at the start of the year).
Let's start with year 1. You have £800 at the start, and at the end you have
£800 x 1.035 = £828.
Now let's think about year 2. You start with £828, and end with
£828 x 1.035 = £856.98
We can also write it like this:
Money at end of year 2 = £828 x 1.035 = £800 x 1.035 x 1.035
Do you see how for each year we earn interest, we just multiply the original £800 by another 1.035?
So, after n years, the total in the account is:
£800 x 1.035n
This makes it easy to work out the total after 7 years, which is just:
£800 x 1.0357 = £1017.82 (rounded to the nearest penny)
To find the interest earned, just subtract the original amount (in this case £800), and we get our answer:
£1017.82 - £800 = £217.82 interestsee more