Problems

Problem 1: A little sailing trip! (answers on a postcard)

You are sailing due south on the sea. You see two lighthouses and you are perpendicular to the first lighthouse. The second lighthouse is 10km due south form the first lighthouse (you find this distance from your chart). You then decide to measure a bearing from your current location to the second lighthouse and find it to be 214⁰. Sometime later you pass the second lighthouse and again you measure the bearing from your new location to the second lighthouse and it is now 283⁰.

Assuming you have travelled in a straight line, what distance have you travelled between the two measurements?    







 

















Problem 3:

A body is found at midnight, on a night when the air temperature is 16 degrees C. Its
temperature is 32 degrees, and after another hour, its temperature has gone down to 30.5
degrees. Estimate the time of death.


Problem 4:

Here is an nice gentle problem to kick off a new season of problems. I found this one from a British Mathematical Olympiad (1993)

Findthe first integer n > 1 such that the average of

12 , 22 , 32 , . . . , n2

is itself a perfect square.

Have a go you might surprise yourself!