How can I get help with the ENGAA Questions Section 1?

[TomK]

Homework Statement

All of the following questions are from ENGAA 2019 (the pre-interview test for Cambridge's Engineering course). The questions are to be attempted without using a calculator. It has two separate sections (1 and 2). The correct answers are written next to each question below. I looked at some (unofficial) worked solutions online (http://www.engineeringadmissionsassessment.com/2019-solutions.html), but it didn't help me understand/finish the questions below.

Relevant Equations

Physics Equations: https://www.ocr.org.uk/Images/536433-data-sheet.pdf

Maths Equations (see page 2 and 3 for formula sheet, ignore the questions): https://www.ocr.org.uk/Images/535673-question-paper-pure-mathematics-and-mechanics.pdf

Section 1:

Q6 - answer: A -

Q11 - answer: B -

Q15 - answer: D -

Q17 - answer: E -

Q19 - answer: E - I got this question correct, but I didn't get an exact answer of '8', so I'm thinking my method was not optimal/has a degree of error? -

Q33 - answer: A -

Q35 - answer: E - https://imgur.com/a/8wjtXjl

Q36 - answer: D - https://imgur.com/a/IbAcLCkSection 2:

Q2 - answer: A - https://imgur.com/a/lshcAeO

Q5 - answer: E - https://imgur.com/a/Oj2lgUe

Q8 - answer: C - https://imgur.com/a/gafezZ5

Q11 - answer: C - https://imgur.com/a/BdkKjct

Q12 - answer: A - https://imgur.com/a/hWVPjov

Q13 - answer: B - https://imgur.com/a/5BNU0uy

Q14 - answer: C - https://imgur.com/a/kwBy3Bm

Q16 - answer: F - https://imgur.com/a/vp58SIn - I think I get why Statement 1 is right. Is it because, when the object is not in-motion, there is no air resistance, therefore weight force will be the only force acting down (which means magnitude of acceleration = g)? I don't know how to prove Statement 2 wrong. Statement 3 is correct, but is it because energy is wasted in every transformation (due to air resistance when in-motion)?

Q18 - answer: B - https://imgur.com/duOp1t8 - no working for this one, since I don't know what angle to choose (for theta) or how to know the other angles in the triangle?Thank you for any help.

 

[haruspex]

Homework Statement:: All of the following questions are from ENGAA 2019 (the pre-interview test for Cambridge's Engineering course). The questions are to be attempted without using a calculator. It has two separate sections (1 and 2). The correct answers are written next to each question below. I looked at some (unofficial) worked solutions online (http://www.engineeringadmissionsassessment.com/2019-solutions.html), but it didn't help me understand/finish the questions below.

This too much for one thread. Please post each question in a separate thread and give more indication of what your issue is with each.
This will allow several different helpers to assist you in parallel.

I will answer this one to go on with:

Q16 - answer: F - I think I get why Statement 1 is right. Is it because, when the object is not in-motion, there is no air resistance, therefore weight force will be the only force acting down (which means magnitude of acceleration = g)? I don't know how to prove Statement 2 wrong. Statement 3 is correct, but is it because energy is wasted in every transformation (due to air resistance when in-motion)?​

1) yes, though the reasoning ought to show not only that it will be free fall acceleration at the top but also that that is the only place it will be free fall.
2) you can answer this by trusting the graph. Distance covered equals area bounded, so the time of return to original position will be where the areas above and below the axis are equal.
3) yes

 

[etotheipi]

For the last one, rewrite $$\begin{align*}\int_{-2}^2 5f(x) dx - \int_{-2}^4 f(x) dx &= \int_{-2}^2 5f(x) dx - \left( \int_{-2}^2 f(x) dx + \int_2^4 f(x) dx \right) = 7 \\

&= \int_{-2}^2 4f(x) dx - \int_{2}^4 f(x) dx = 7\end{align*}$$By what constant can you multiply this equation by so that, when you then subtract it from the first equation, you get another equation only involving $\int_2^4 f(x) dx$?

 

[berkeman]

This too much for one thread. Please post each question in a separate thread and give more indication of what your issue is with each.
This will allow several different helpers to assist you in parallel.

Agreed, but please figure out each problem before posting the next. The parallelism model is close to spamming (like this thread here). Thanks. This thread is locked.