R8 | Maths Made Easy

R8

QUESTION:An aeroplane travels at an average speed of 230 kilometres per hour for a total journey time of 414 minutes. Work out the total distance covered by this aeroplane.

 

QUESTION: A pressure of 40 N/M^2 is exerted evenly on the area of the triangle shown here. Calculate the force being applied to exert this amount of pressure.

ANSWER:

If we cover up d in the triangle, we see that we will have to multiply s by t to get our answer. However, the units don’t match up – we need to convert the minutes to hours, which we will do by dividing it by 60.

t=414\div 60=6.9\text{ hours}

Now, we can do the multiplication:

\text{distance covered }=d=230\times 6.9=1,587\text{ km}

 

ANSWER: Covering up F on the triangle,

We see that we need to multiply p (pressure) by A (area). To do this, we need to find the area of the triangle above. Before that, however, notice that the sides of the triangle are measured in centimetres which doesn’t match up with the “Newtons per metres squared” in the question. So, we will convert the dimensions of the triangle into metres by dividing by 100:

\text{height }=80\div 100=0.8\text{ m}

\text{base }=150\div 100=1.5\text{ m}

Now we can calculate the area of the triangle:

\text{area }=\dfrac{1}{2}bh=\dfrac{1}{2}\times0.8\times1.5=0.6\text{ m}^2

Therefore, we get that the force being applied is

F=p\times A=40\times 0.6=24\text{ N}