# Help - Problems that i don't understand

## Main Question or Discussion Point

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) im 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

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?