A stone is thrown upwards with a speed of v metres per second. The stone reaches a maximum height of h metres. h is directly proportional to v^2. When the stone is thrown at 10m/s, max height is 5m. Work out the maximum height reached when v = 24.
(Question 20 in AQA calculator paper from November 2017)This question is really wordy, so the first thing we want to do is condense all the information we are given into more manageable equations! The first important piece of information the question tells us is that 'h is directly proportional to v2' . This sounds scary, but all it means is that the height increases by a constant multiple for every increase in the value of (velocity)2. Instead of complicating this with words, we introduce the constant multiple k and create an equation that we can use to work out the answer.Step 1/ Create an equation that will look like this:height= k (velocity)2 or h= kv2 Step 2/ We now need to work out the value of k. We can do this by plugging in the values that we are given (when the stone is thrown at 10m/s, the maximum height reached is 5metres, therefore h=5 when v=10)(5)= k(10)2expand to get : 5=100ktherefore: k=0.05 (or 1/20)Step 3/ We now have to work out what the max height is when the velocity is 24. We can do this by plugging 24 back into the initial equation, where the value of k is 0.05:h=0.05v2 h=0.05(24)2 then use your calculator to get: h=28.8metres and you're done!
