Help - Problems that i don't understand

[Hurly]

1) Amateur astronomers often approximate angles with an arm out-
stretched. With the hand in this position, one nger's width is approximately
2, the width of your hand at the knuckles is approximately 10 and your
hand fully spanned is approximately 20. You are on the shore and you see a
boat. With your arm outstretched, the height of its mast is 1 nger's width.
You also know that this boat's mast is 10 metres in height. How far away
is the boat? 30 seconds later you notice the mast is now 2 nger widths in
height. How fast is the boat sailing towards you? Now convert this speed
into knots (look it up).

2) A tin can manufacturer wants to minimise the cost of metal in a can
of volume 500 cm3. To do this you need to minimise the surface area of the
cylindrical can. Determine the radius and height of such a can.

3) On a topographic map, contour lines join points of equal altitude. If
you followed a contour, you would not go up or down in elevation. Hopefully
you can see then that the steepest incline/decline would be perpendicular to
the contours. Suppose I want to know what direction to climb up a mountain
(I am rogaining in a mountainous region), I am at -36:41258 N, 148:355248
E and I can see that on the map the contour nearest to me is a straight line
from -36:405948 N 148:354883 E to -36:423216 N 148:3566 E. What line
should walk along in the North-East plane? Also for each metre I move to
the North, how many metres should I move to the East?


- I've had numerous attempts at these questions but can't get a grasp on it
1) confuses me
2) I am not sure about because i don't think i have been given enough info
3)i've drawn a little diagram of it but need help

Thanks in advance for your help =)

 

[Diffy]

If I were you I would ask that this be moved to a forum where people are willing to give homework help. Even if this is independent study this is not the appropriate forum.

I'll give you some hints.

For 1 draw a triangle. You know the height of the mask, and an angle. It should be as simple as using trig to solve.

For number 2 you should be able to find 2 formulas. One for volume and one for surface area. Then it just becomes a regular calculus problem.

For number 3 if you have drawn yourself a picture, do you know what it is you are actually trying to do? can you draw the line you think you should walk?