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Math mechanics alevel question summer 2016 M2 52

9709/m/j/52/16
Anyone know how to do (ii)?

I got an answer for (i) which is 4 m. (−8 = 2x − x^2). I cannot do (ii). Below is the solution for (ii), but I don't understand it at all. How does tan^-1(2) come from? Does 2 come from 8/4 (Sy/Sx)? This does not seem correct to me.

Also, I am not sure how the picture of this should be looked like? Should it be like the left or the right one? From what I understand, I think it should be the one on the right. However, from the solution, it seems to be the left one that is correct.
Please help! Thank you

Original post by anonymo007

...

For any function y=f(x), dy/dx is the tan of the angle that the curve makes with the +ve x-axis (up being positive).

So, in this case, dy/dx = 2-2x, which =2 when x=0.

So, tan of angle of projection = 2. Hence....

Also,dy/dx > 0 when x=0; so, the curve goes up initially.