Hi all, So I'm struggling to work out the answer to part B, C and D. I've attached the picture of the question and my working for the first part of the question.
Hi all, So I'm struggling to work out the answer to part B, C and D. I've attached the picture of the question and my working for the first part of the question.
TIA!
For part b (i) you are on the right track...
1=α−10cos(0)+3sin(0)
What are the value of cos(0) and sin(0) ?? Hence alpha is...?
For b (ii) you need to incorporate the fact that 10cosθ−3sinθ=109cos(θ+16.7) into H=α−(10cos(80t)−3sin(80t))... how can you rewrite H using this??
Also to point out, for your answer to question 1a, the identity is:
Rcos(a+b)=Rcos(a)cos(b)−Rsin(a)sin(b).
However, the rest of your answer for question 1a is fine. -----------------------------------------------------------------------------------------------------------------------------------------------------------
For question 1c, you found the equation for height H has form:
α−109cos(t+16.7∘),
where α is to be found.
Can you find the time that the passenger has the greatest height for the first time (call this tmax). (Ideally found by knowing how cos behaves).
Then cos is a periodical function so cos has a maximum/minimum again after T units (e.g. cos(0+T)=cos(0)=1, for a particular value of T).
Are you able to find T and use this to find the time needed (where the passenger is at the maximum height for the second time)?
What are the value of cos(0) and sin(0) ?? Hence alpha is...?
For b (ii) you need to incorporate the fact that 10cosθ−3sinθ=109cos(θ+16.7) into H=α−(10cos(80t)−3sin(80t))... how can you rewrite H using this??
So would I have to cos^-1 and sin^-1 (which are 90 and 0) to get alpha or would I use the actual values of cos(0) and sin(0) (which are 1 and 0)? And then for b(ii) I have substituted 80t into sqrt {109}cos (theta + 16.7) so it's sqrt {109}cos(80t + 16.7) is that right?
So would I have to cos^-1 and sin^-1 (which are 90 and 0) to get alpha or would I use the actual values of cos(0) and sin(0) (which are 1 and 0)? And then for b(ii) I have substituted 80t into sqrt {109}cos (theta + 16.7) so it's sqrt {109}cos(80t + 16.7) is that right?
Why would you inverse cos or sin?? cos(0)=1 and sin(0)=1 so just stick them in.
Yes its right, so rewrite H in terms of this sqrt {109}cos(80t + 16.7)
You got the right eqn for H now, but i dont understand what you are doing afterwards.
Since H is of the form (constant) - (other costant)*(cos function) you need to realise that max height is given when this result is maximised. Clearly, the two constant stay the same so its just the matter of focusing on (cos function) and seeing what value of it will give us max height. What are the two extreme values of the (cos function) ?? For which do we get max height ??
You got the right eqn for H now, but i dont understand what you are doing afterwards.
Since H is of the form (constant) - (other costant)*(cos function) you need to realise that max height is given when this result is maximised. Clearly, the two constant stay the same so its just the matter of focusing on (cos function) and seeing what value of it will give us max height. What are the two extreme values of the (cos function) ?? For which of these two do we get max height ??
Also to point out, for your answer to question 1a, the identity is:
Rcos(a+b)=Rcos(a)cos(b)−Rsin(a)sin(b).
However, the rest of your answer for question 1a is fine. -----------------------------------------------------------------------------------------------------------------------------------------------------------
For question 1c, you found the equation for height H has form:
α−109cos(t+16.7∘),
where α is to be found.
Can you find the time that the passenger has the greatest height for the first time (call this tmax). (Ideally found by knowing how cos behaves).
Then cos is a periodical function so cos has a maximum/minimum again after T units (e.g. cos(0+T)=cos(0)=1, for a particular value of T).
Are you able to find T and use this to find the time needed (where the passenger is at the maximum height for the second time)?
For question 1d, if the ferris wheel is faster, you expect more cycles.
How do we get more cycles in a cos graph (under a certain time)?
Does this help?
It kind of helps, but still a bit confused about the last 2 questions. (thank you for letting me know about the mistake I made in part a, I didn't realise I'd put cos instead of sin)